ELECTRIC  LIGHTING 

AND  MISCELLANEOUS  APPLICATIONS 
OF  ELECTRICITY 


ELECTRIC  LIGHTING 


AND  MISCELLANEOUS  APPLICATIONS 
OF  ELECTRICITY 


A  TEXT  BOOK  FOR 
TECHNICAL  SCHOOLS  AND  COLLEGES 


BY 

WILLIAM  SUDDARDS  FRANKLIN 


¥ork 
THE  MACMILLAN  COMPANY 

LONDON  :   MACMILLAN  &  CO.,  LTD. 
1912 

All  rights  reserved 


COPYRIGHT  1912 
BY   THE   MACMILLAN   COMPANY 


Set  up  and  electrotyped.     Published  May,  1912 


PRESS  OP 

THE  NEW  ERA  PRINTING  < 
LANCASTER.  PA. 


PREFACE. 

This  book  is  intended  to  be  a  companion  volume  to  Dynamos 
and  Motors. 

In  the  preparation  of  these  two  volumes  especial  attention  has 
been  given  to  the  physical  principles  which  underlie  operating 
engineering,  and  but  little  attention  has  been  given  to  the 
principles  of  design. 

April  22,  1912. 


242234 


TABLE  OF  CONTENTS. 


CHAPTER  I. 

PAGES 
Installation  and  Operation  Costs I-  35 

CHAPTER  II. 
Electric  Distribution  and  Wiring 36-  76 

CHAPTER  III. 
Alternating-current  Lines 77-  85 

CHAPTER  IV. 
Photometry 86-125 

CHAPTER  V. 
Electric  Lamps,  Lamp  Shades  and  Reflectors 126-155 

CHAPTER  VI. 
Interior  Illumination 156-170 

CHAPTER  VII. 
Street  Illumination 171-183 

CHAPTER  VIII. 
Electrolysis  and  Batteries 184-225 

CHAPTER  IX. 
Telegraph  and  Telephone 226-256 

APPENDIX  A. 
Dielectric  Stresses 257-276 

APPENDIX  B. 
Problems 277-295 


Vll 


IMPORTANT   INDEXES   AND   TABLES  AND   SPECIAL 
PUBLICATIONS. 

Engineering  Index  Annual,  published  by  The  Engineering  Magazine,  London. 
Science  Abstracts,  published  by  E.   &   F.  N.  Spon,  London,  Series  A,  Physics; 

Series  B,  Electrical  Engineering. 

Science  Abstracts  is  issued  by  the  Institution  of  Electrical  Engineers  of  Great 
Britain  in  association  with  the  Physical  Society  of  London,  and  with  the  cooper- 
ation of  the  American  Physical  Society,  the  American  Institute  of  Electrical  En- 
gineers, and  the  Associazione  Elettrotecnica  Italiana. 

Physico-Chemical  Tables,  by  John  Castell-Evans,  Chas.  Griffen  &  Co.,  London. 
Physikalisch-Chemische  Tabellen,  by  Landolt  &  Bornstein,  Julius  Springer,  Berlin. 
Manufacturers'  Bulletins  and  Circulars  contain  a  great  deal  of  important  in* 
formation. 


ELECTRIC  LIGHTING, 


CHAPTER   I 

INSTALLATION  AND  OPERATION  COSTS  AND  THE  SELLING  PRICE 
OF  ELECTRICAL  ENERGY. 

i.  General  statement. — From  one  point  of  view  engineering 
is  a  composite  of  all  the  physical  sciences,  and  from  another 
point  of  view  it  is  a  branch  of  the  science  of  economics.  Any 
elementary  treatise  on  engineering  should,  however,  be  chiefly 
devoted  to  purely  physical  problems  inasmuch  as  the  student 
must  become  familiar  with  engineering  as  a  branch  of  physical 
science  before  he  can  possibly  undertake  as  a  practising  engineer 
to  choose  that  particular  physical  solution  of  an  engineering 
problem  which  will  best  meet  the  requirements  of  economy. 

The  economic  problem  is  in  every  case  to  produce  satisfactory 
results  at  a  minimum  of  ultimate  cost,  and  this  is  always  a  very 
complicated  problem  inasmuch  as  the  cost  of  erection  and  main- 
tenance of  engineering  works  and  the  value  of  the  service  rendered 
thereby  are  both  dependent  upon  minute  variations  of  local 
conditions,  they  both  fluctuate  from  year  to  year  with  the  varying 
stress  of  business  activity  and  they  both  change  with  every 
improvement  in  industrial  processes. 

The  first  estimate  of  the  cost  of  any  engineering  undertaking 
is  usually  based  upon  general  statistics  of  the  cost  of  similar 
undertakings,  and  the  final  cost  is  determined  by  the  bids  of 
contractors  who  have  had  some  experience  in  the  particular  line 
of  work  and  whose  margin  of  profit  must  in  general  be  great 
enough  to  cover  the  many  uncertain  items  that  always  appear  in 
any  new  undertaking. 


2  ELECTRIC    LIGHTING. 

The  following  data  on  the  cost  of  installing  and  operating 
steam  and  electric  plants  are  averages  based  upon  the  record  of  a 
large  number  of  actual  cases,  and  the  cost  of  a  given  station  may 
depart  considerably  from  these  figures  on  account  of  peculiar 
local  and  temporary  conditions. 

THE  STUDENT  IS  WARNED  THAT  AVERAGES  ARE  ALWAYS  MIS- 
LEADING IN  COMPLICATED  MATTERS  LIKE  COSTS,  BECAUSE  TO  TAKE 
AN  AVERAGE  IS  TO  ELIMINATE  EVERY  ELEMENT  OF  DIFFERENCE 
BETWEEN  INDIVIDUAL  CASES,  AND  THESE  DIFFERENCES  ARE  VERY 
GREAT.*  THE  GENERAL  ESTIMATES  WHICH  ARE  GIVEN  IN  THIS 
CHAPTER  WILL  BE  WORSE  THAN  USELESS  IF  THE  ONE  WHO  USES 
THEM  DOES  NOT  CONSIDER  THE  PECULIAR  FEATURES  OF  THE  PAR- 
TICULAR CASE  UNDER  CONSIDERATION. 

2.  Cost  of  steam  power. f — The  ordinates  of  the  curve  A    in 

*  In  this  connection  the  student  should  read  R.  S.  Hale's  article  "The  Real 
Theory  of  Real  Rates"  in  the  General  Electric  Review  for  April,  1911,  Vol.  XIV, 
pages  157-169. 

t  The  data  from  which  the  curves  in  Figs,  i  and  2  are  plotted  are  taken  from  a 
paper  by  William  O.  Weber,  The  Engineer  (Cleveland),  Vol.  XI,  page  145,  February 
2,  1903- 

Important  data  on  the  cost  of  steam  power  and  on  the  cost  of  electrical  equip- 
ment are  given  by  C.  E.  Emery,  Transactions  American  Institute  of  Electrical 
Engineers,  Vol.  XII,  pages  358-389,  1895;  by  H.  A.  Foster,  Transactions  American 
Institute  of  Electrical  Engineers,  Vol.  XIV,  pages  385-421,  1897;  and  by  R.  C.  Car- 
penter, Electrical  World,  Vol.  XLIII,  page  1016,  May  28,  1904. 

An  important  paper  on  the  cost  of  power  in  very  large  plants  is  given  by  H.  G. 
Stott,  Transactions  American  Institute  of  Electrical  Engineers,  Vol.  XXVIII,  pages 
1479-1502,  December,  1909.  This  paper  gives  data  as  to  cost  of  plants  and  as 
to  fuel  and  operation  costs,  and  it  includes  plants  driven  by  reciprocating  steam 
engines,  by  steam  turbines  and  by  gas  engines. 

The  cost  of  power  in  industrial  plants  where  exhaust  steam  may  be  used  for 
heating  is  discussed  by  John  C.  Parker,  Proceedings  American  Institute  of  Electrical 
Engineers,  March,  1911,  pages  467-483;  and  by  A.  E.  Hibner,  Proceedings  American 
Institute  of  Electrical  Engineers,  March,  1911,  pages  485-503. 

The  economics  of  a  small  producer-gas  plant  are  discussed  by  F.  C.  Tyron, 
Power  (New  York),  Vol.  XXVIII,  pages  619-620,  April  21,  1908.  The  economics 
of  a  suction-gas  plant  are  discussed  by  P.  W.  Robinson,  Electrician  (London), 
Vol.  LXI,  pages  898-901,  September  25,  1908.  A  description  of  the  equipment  of 
a  gas-engine  electric  plant  together  with  data  as  to  operation  costs  of  same  is  given 
by  E.  B.  Latta,  Jr.,  Proceedings  American  Institute  of  Electrical  Engineers,  Vol. 
XXIX,  pages  475~507»  April,  1910. 


COSTS   AND   SELLING   PRICE.  3 

Fig.  I  give  the  approximate  total  cost  per  horse- power  capacity, 
of  boiler  and  engine  plants  of  various  sizes,  including  buildings, 
chimneys  and  all  accessories,  and  the  ordinates  of  curve  B  give 
the  approximate  coal  consumption  in  pounds  per  horse-power- 
hour.* 

The  ordinates  of  the  curves  C,  D,  E,  F  and  G  in  Fig.  2 
give  the  costs  per  horse-power-year  (308  days  of  10  hours  each) 
of  the  following  items : 

Curve  C.  Fixed  charges  per  horse-power-year.  This  item  is 
'reckoned  at  14  per  cent,  of  the  total  investment,  and  it  includes 
interest  at  six  per  cent.,  depreciation!  at  4  per  cent.,  repairs  at  2 
per  cent.,  insurance  and  taxes  at  two  per  cent. 

Curve  D.  Cost  of  coal  per  horse-power-year  at  $4.00  per  ton 
of  2,000  pounds. 

Curve  R.     Wages  per  horse-power-year. 

Curve    F.     Cost  of  oil  and  supplies  per  horse-power-year. 

Curve   G.     Total  cost  per  horse-power-year. 

These  curves  are  based  on  the  assumption  that  engines  of  the 

The  cost  of  water  power  is  discussed  in  the  Mechanical  Engineer  (Manchester, 
England),  Vol.  XII,  page  694,  November  21,  1903.  The  comparative  cost  of 
steam  and  water  power  is  discussed  by  H.  von  Schon,  Engineering  Magazine 
(London),  Vol.  XXX,  pages  35-48,  184-194,  353-380,  and  611-622,  May  to  July, 
1907.  See  also  W.  O.  Webber,  Engineering  Magazine,  Vol.  XXX,  pages  889-893, 
September,  1907.  A  paper  on  hydro-electric  plants  by  H.  L.  Doherty  together 
with  a  very  complete  discussion  of  the  subject  is  given  in  Transactions  American 
Institute  of  Electrical  Engineers,  Vol,  XXVIII.  pages  1361-1478,  December,  1909. 

*  The  coal  consumption  in  a  large  steam-turbine  power  plant  is  considerably 
less  than  the  coal  consumption  given  by  the  ordinates  of  curve  B  in  Fig.  i,  and  the 
coal  consumption  in  a  gas-engine  plant  is  less  than  the  coal  consumption  in  a  steam- 
turbine  plant.  See  paper  by  H.  G.  Stott,  Transactions  American  Institute  of 
Electrical  Engineers,  Vol.  XXVIII,  pages  1479-1502,  December,  1909;  and  a 
paper  by  H.  G.  Stott  and  J.  S.  Pigott,  Proceedings  American  Institute  of  Electrical 
Engineers,  Vol.  XXIX,  pages  1455-1501,  September,  1910. 

f  Depreciation  is  a  very  uncertain  item.  The  estimate  for  the  whole  plant  of  4 
per  cent,  per  year  is  perhaps  too  low.  The  depreciation  of  buildings  is  less  than 
4  per  cent,  and  the  depreciation  of  electrical  machinery  is  perhaps  more  than  4 
per  cent.,  but  the  depreciation  of  boilers  and  engines  is  certainly  considerably 
greater  than  4  per  cent,  per  year. 

See  paper  by  Henry  Floy  for  a  detailed  discussion  of  depreciation:  Proceedings 
American  Institute  of  Electrical  Engineers,  Vol.  XXX,  pages  1143-1185,  June,  1911. 


ELECTRIC    LIGHTING. 


100 


|J 

s, 

i 

i 

t 


100    200    300    40O    500    000 

Horse-power  of  engine. 
Fig.  1. 


700      boo      900 


80 


70 
6o 

40 

20 


IOO         2OO         3OO         400 


Horse-power  of  engine* 
Fig.  2. 


COSTS    AND   SELLING   PRICE.  5 

smaller  sizes  are  simple  non-condensing  engines  of  the  Corliss 
type,  that  engines  of  the  medium  and  larger  sizes  are  simple  con- 
densing engines,  and  that  the  engines  of  the  largest  sizes  are 
compound  condensing  engines. 

The  wages  in  a  loo-horse-power  plant  are  taken  to  be  as  fol- 
lows: An  engineer  at  $2.50  per  day  and  a  fireman  at  $1.50  per 
day,  which  would  amount  to  about  $1,200  per  year.  In  a  1,000- 
horse-power  plant  the  wages  are  taken  to  be  as  follows:  One 
engineer  at  $3.00  per  day,  one  assistant  engineer  at  $2.00  per 
day  and  three  men  in  the  boiler  room  during  the  day  and  one 
night  watchman  at  $1.50  per  day  each,  and  the  total  amount 
would  be  about  $3,500  per  year. 

The  cost  of  coal  per  horse-power-year  at  any  given  price  per 
ton  may  be  easily  determined  from  curve  D,  Fig.  2,  the  ordinates 
of  which  represent  the  cost  of  coal*  per  horse-power-year  at  $4.00 
per  ton,  and  the  total  cost  per  horse-power-year,  as  given  by 
curve  Gj  may  be  corrected  accordingly. 

It  is  important  to  remember  that  the  cost  of  power  as  given  by 
curve  G,  Fig.  2,  is  based  on  the  assumption  that  the  engines 
are  working  at  full  load  for  10  hours  per  day,  308  days  in  the  year. 
When  a  plant  operates  at  a  fraction  of  its  full-load  capacity  the 
cost  per  horse-power-hour  is  increased  as  explained  in  Art.  4. 

3.  Cost  of  electrical  power  at  the  switch  board. — The  ordi- 
nates of  the  curve  H,  Fig.  3,  give  the  capacities  in  kilowatts  of 
electrical  equipments  corresponding  to  various  horse-power  ca- 
pacities of  engine  plants.  This  curve  is  not  exactly  a  straight 
line  inasmuch  as  the  efficiency  of  a  large  electric  generator  is 
greater  than  the  efficiency  of  a  small  electric  generator  of  the 
same  design. 

The  following  estimate  of  the  cost  of  electrical  power  at  the 
switch  board  is  based  upon  the  cost  of  steam  power  as  given  in 
Figs.  I  and  2  and  upon  the  assumption  that  the  plant  operates 
at  full  load,  10  hours  per  day  for  308  days  per  year.  The  ap- 

*  A  good  quality  of  coal  giving  14,500  B.T.U.  per  pound  is  here  referred  to. 


6  ELECTRIC   LIGHTING. 

proximate  cost  of  the  electrical  part*  of  the  equipment  in  dollars 
per  kilowatt  of  station  capacity  may  be  obtained  by  dividing 
the  ordinate  of  curve  /,  Fig.  4,  by  0.14.  This  cost  ranges 
from  about  $45.00  per  kilowatt  for  a  loo-kilowatt  station  to  about 
$35 -00  per  kilowatt  for  a  yoo-kilowatt  station.  The  cost  of 


700 

600 
500 
400 
300 

200 
100 

s 

x 

gene™ 

^ 

^ 

•8 

x 

1 

42 

x 

X 

3 

X 

x 

IT, 

X 

X 

X 

• 

loo      zoo      300      400      500      600      7°o      °oo      900 
Horse-power  of  engine, 

Fig.  3. 

additional  labor  required  by  the  electrical  part  of  the  plant  is 
about  25  per  cent,  of  the  cost  of  labor  for  the  steam  plant  alone, 
and  the  additional  cost  of  oil  and  supplies  is  about  40  per  cent, 
of  the  cost  of  this  item  for  the  steam  plant  alone. 

The  curves  in  Fig.  4  show  an  approximate  analysis  of  the  cost 
of  electrical  power  as  follows: 

Curve  /  shows  the  cost  of  steam  power  per  kilowatt-year  of 
electrical  output  (determined  from  curve  G  of  Fig.  2,  using 
Fig.  3). 

Curve  /  shows  the  fixed  charges  on  the  electrical  equipment 
per  kilowatt-year.  This  item  is  reckoned  at  14  per  cent,  of  the 
cost  of  the  electrical  equipment,  and  it  includes  interest  at  6 

*  Not  including  the  distributing  system.     See  Art.  5. 


COSTS   AND   SELLING   PRICE.  7 

per  cent.,  depreciation  4  per  cent.,  repairs  2  per  cent.,  insurance 
I  per  cent.,  and  taxe$  I  per  cent. 

Curve  K  shows  the  cost  per  kilowatt-year  for  attendance 
(labor)  of  electrical  equipment  in  "addition  to  attendance  of  steam 
plant. 

Curve  L  shows  the  cost  per  kilowatt-year  of  oil  and  supplies 
for  electrical  equipment. 


300          400          500         600          7°o 
Kilowatts  capacity  of  generator^ 
Fig.  4. 

Curve  M  shows  total  cost  per  kilowatt-year  of  electrical 
output. 

Curve  N  shows  the  total  cost  per  kilowatt-hour  of  electrical 
output. 

4.  Load  factor  and  its  influence  on  the  cost  of  power.* — The 

discussion  of  cost  of  power  which  is  given  in  the  foregoing  articles 

*  A  very  complete  table  of  costs  of  electric  power  at  the  switchboard  showing 
a  wide  range  of  load  factors  is  given  by  R.  W.  Conant,  Electrical  World,  Vol.  XXXII, 
pages  313-319,  September  24,  1898.  See  also  Street  Railway  Journal,  Vol.  XVIII, 
page  827,  December  7,  1901,  and  Vol.  XXV,  pages  126-128,  January  21,  1905; 
and  Street  Railway  Review,  Vol.  XIII,  pages  185-198.  April,  1903. 


8 


ELECTRIC   LIGHTING. 


is  based  upon  the  assumption  of  continuous  operation  of  a  power 
plant  at  full  load.  As  a  matter  of  fact,  however,  the  demand  for 
power  always  fluctuates  greatly  so  that  a  power  plant  which  is 
designed  to  deliver  the  maximum  amount  of  power  demanded 
must  be  operated  for  a  large  portion  of  the  time  at  a  fraction  of 
its  rated  capacity. 


capacity  of  gas  engine  plant 


capacity  of  hydraulic    plant 


capacity  of  steam  engine  plant 


12     i_    2     3     4     5     6     7     8     9    10   ii    12     i      23     4     55     7     3    9    ">    11    12 
Fig.  5.     Winter  and  summer  load  curves  of  lighting  plant. 

The  average  load  on  a  plant  (in  kilowatts)  divided  by  the 
capacity  of  the  plant  in  kilowatts  is  called  the  load  factor.  For 
example,  a  465-kilowatt  plant*  operating  14  hours  per  day  365 
days  per  year  delivers  a  total  of  464,000  kilowatt-hours,  so  that 


the   average   load   is 


464,000 
14X365 


=  90.8   kilowatts,  and   the   load 


The  effect  of  load  factor  on  the  cost  of  power  is  discussed  by  W.  M.  Archibald, 
Electrical  World,  Vol.  XLV,  pages  303-305.,  February,  1905. 

A  paper  by  H.  G.  Stott,  Transactions  American  Institute  of  Electrical  Engineers, 
Vol.  XXVIII,  pages  1479-1502,  December,  1909,  takes  account  of  the  influence 
of  load  factor  on  the  cost  of  power.  The  curves  given  in  Fig.  8  are  taken  from  this 
paper. 

*  See  page  32. 


COSTS   AND    SELLING   PRICE. 


90.8 
factor  is  ~~TT  or  0.195 

•     4 


In  specifying  a  load  factor  it  is  impor- 


tant to  give  also  the  average  daily  run  in  hours. 

Figure  5  shows  typical  summer  and  winter  load-curves  on  a 
power  plant  supplying  power  for  lighting;  Fig.  6  shows  a  typical 
load-curve  on  a  power  plant  supplying  power  for  the  operation 


capacity  of  gas  engine  plant 

/ 

\ 

__t-  _J~J  L_|  I  I-  -j 
—  capacity  of  hydraulic 
\      \     iplant      1      i 

U- 

-^ 

^-- 

._. 

__. 

/_ 

\-L 

-- 



-- 



/ 

X 

,/ 

\ 

• 

cap 

aci 
eni 

ty 
fin 

of 
e  p 

ste 
'an 

aw 
i 

/ 

\ 

\1  '~~ 

/ 

V 

\ 

5 
.* 

* 

/ 

\ 

\\ 

1 

I 

| 

/ 

c 

T3 

/ 

\ 

/ 

\l 

/ 

\ 

I 

K 

—• 

"-" 

I 

^ 

A.M. 

hour 

P.M. 

23456789     10  11    12    i      23455739    10    11    12 
Fig.  6.     Load  curve  of  plant  supplying  motors  in  manufacturing  district. 

of  motors  in  a  manufacturing  district;  and  Fig.  7  shows  typical 
load-curves  on  a  power  plant  supplying  power  to  a  large  city 
electric  railway  system. 

The  horizontal  dotted  lines  in  Figs.  5,  6  and  7  show  suitable 
power  ratings  of  plants  for  the  respective  load  curves.  A  prop- 
erly designed  steam  plant  has  a  very  large  overload  capacity, 
a  hydraulic  plant  has  a  small  overload  capacity,  and  a  gas- 
engine  plant  has  practically  no  overload  capacity.  Therefore 
the  "peak  of  the  load"  (maximum  load)  may  be  25  or  30  per 
cent,  in  excess  of  the  rated  capacity  of  a  steam  plant,  not  more 
than  5  or  10  per  cent,  in  excess  of  the  rated  capacity  of  a  hy- 
draulic plant,  and  not  at  all  in  excess  of  the  rated  capacity  of  a 


10 


ELECTRIC    LIGHTING. 


gas-engine  plant.  A  further  consideration  which  bears  upon 
the  proper  rating  of  a  power  plant  is  the  probability  of  excessive 
demand  for  power  on  special  occasions.  Thus  an  excessive  de- 
mand for  power  is  likely  to  occur  in  a  street  railway  system,  and 
it  is  for  this  reason  that  the  rated  plant  capacities  in  Fig.  7  are 


V 
I 

a  ~ 

I 
•s 


1 


capacity  of  gas  engine  plant 


capacity  of  hydraulic  plan 


steam  engine 


\: 


June. 


noon 


plant 


P.M. 


12      2       4      6      8      10      13      2       46       8       10     12 
Fig.  7.     Winter  and  summer  load  curves  of  electric  railway  plant. 

larger  as  compared  with  the  normal  peak  of  the  load  than  in 
Figs.  5  and  6. 

The  load  factor  on  an  ordinary  electric  lighting  station  may 
be  as  low  as  0.15  for  a  small  plant  in  a  small  town  where  there  is 
but  little  lighting  during  the  day.  If  the  plant  supplies  current 
for  motors  during  the  day  to  any  considerable  extent  the  load 
factor  may  be  as  large  as  0.40.  The  load  factor  of  a  plant  which 
supplies  current  for  electric  railways  may  be  as  low  as  0.20  or 
0.30  when  there  are  but  few  cars  in  operation,  or  as  high  as  0.40 
or  0.50  when  many  cars  are  operated.  When  a  single  large  power 
plant  supplies  power  for  lighting,  for  manufacturing  and  for 


COSTS   AND   SELLING   PRICE.  II 

street  railways,  the  combined  demand  for  power  is  much  more 
nearly  uniform  than  /or  either  kind  of  service  alone,  and  the 
load  factor  in  this  case  is  sometimes  as  large  as  0.60  or  even  larger. 

The  influence  of  load  factor  on  the  cost  of  power  is  illustrated 
by  the  following  example:  Consider  a  1,000  horse-power  electric 
light  station  representing  a  total  investment  of  $100,000,  not 
including  the  distributing  system.  The  fixed  charge  (interest, 
depreciation,  repairs,  insurance  and  taxes)  is,  say,  14  per  cent, 
on  the  total  investment,  or  $14,000  per  year.  If  the  station  were 
run  at  full  load  day  and  night  the  year  round,  the  running  ex- 
penses would  be  approximately  as  follows :  (a)  wages  of  one  chief 
engineer  and  superintendent  at  $5.00  per  day,  two  assistant 
engineers  at  $2.50  per  day,  three  helpers  in  the  engine  room  at 
$1.50  per  day  and  six  men  in  the  boiler  room  at  $1.50  per  day, 
making  a  total  of  $8,600  per  year;  (b)  coal  at  2.5  pounds  per 
horse-power-hour  at  $4.00  per  ton  would  amount  to  about 
$43,700  per  year;  and  (c)  petty  stores  would  amount  to  about 
$6,500  per  year.  The  total  annual  expense  of  $72,800  would  be 
the  cost  of  approximately  6,000,000  kilowatt-hours,  which  would 
be  at  the  rate  of  1.22  cents  per  kilowatt-hour  delivered  at  the 
switchboard. 

If  the  station  were  run  night  and  day  the  year  around  at  an 
average  load  equal  to  0.25  of  its  full-load  capacity,  the  running 
expenses  would  be  approximately  as  follows:  (a)  wages,  one 
engine  room  helper  and  three  firemen  less  than  before,  would 
amount  to  $5,100  per  year;  (b)  the  coal  consumption  of  a  1,000- 
horse-power  engine  running  at  one  quarter  load  would  be  about 
6  pounds  per  horse-power-hour,  therefore,  the  cost  of  coal  would 
be  about  $26,200  per  year;  and  (c)  petty  stores  would  be  about 
$5»5oo  Per  year.  The  total  annual  expense  of  $51,400  would  be 
the  cost  of  1,500,000  kilowatt-hours  which  would  be  at  the  rate 
of  3.43  cents  per  kilowatt-hour  delivered  at  the  switchboard. 

This  example  illustrates  the  great  importance  of  load  factor 
as  a  condition  affecting  the  cost  of  power.  Certain  items  of 
expense  are  nearly  constant  whatever  the  load  on  the  station  may 


12 


ELECTRIC   LIGHTING. 


be.  The  sum  of  these  items  (interest,  depreciation,  taxes  and 
administrative  expenses)  is  called  the  fixed  charge.  When  a 
station  is  operated  at  light  load  the  item  of  wages  may  be  some- 
what reduced  especially  if  the  station  is  shut  down  during  certain 
hours  each  day,  also  the  item  of  fuel  is  reduced;  but  neither  is 
reduced  in  proportion  to  the  reduction  of  load.  Therefore  the 
cost  per  kilowatt-hour  increases  greatly  with  decrease  of  load 
on  the  station.  The  following  table  shows  the  increasing  cost 

TABLE  SHOWING  EFFECT  OF  LOAD  FACTOR  ON  COST  OF  POWER. 
Costs  per  kilowatt-hour  in  cents*  (i5o-kilowatt  steam  plant). 


Load-factor. 

O.2. 

0.4. 

0.6. 

0.8. 

Interest  on  investment  
Depreciation 

1.70 
I    2O 

0.85 

o  60 

O..S7 

O  44, 

0.42 
O  1"? 

Management  and  taxes 

I   ^O 

O  71? 

O  ^O 

o  40 

Repairs 

I  OO 

o  c  c 

o  40 

o  30 

Fuel 

I   ^O 

I  A.O 

I  ^O 

Labor 

I   ^O 

I  20 

I  OO 

Petty  stores 

o  20 

O  I  r 

O  IO 

o  08 

Total  cost  per  kilowatt-hour  in  cents. 

8.60 

5-56 

4.31 

3.63 

per  kilowatt-hour  (delivered  to  the  consumer,  see  Art.  5)  with 
decrease  of  load  factor  as  estimated  by  B.  J.  Arnold.  |  These 
figures  refer  to  a  power  station  having  a  full-load  capacity  of  about 
150  kilowatts.  Figure  8  shows  the  influence  of  load  factor  (per 
cent,  load)  on  the  cost  of  electrical  energy  as  estimated  by  H.  G. 
StottJ  for  a  large  steam-turbine  plant  costing  $75  per  kilowatt  of 
rated  capacity.  The  ordinates  of  curve  A  show  the  cost  of  coal 
[high  grade  coal  (14,500  B.T.U.  per  pound)  at  $3.00  per  ton] 
and  water  per  kilowatt-hour,  the  ordinates  of  curve  B  show  the 
total  operation  cost  (coal  and  water,  boiler  and  engine  room 
labor,  coal  and  ash  handling,  oil  and  engine  room  supplies) 

*  Costs  in  this  table  include  interest,  depreciation,  repairs,  etc.,  on  the  dis- 
tributing system.  See  Art.  5. 

^Electrical  World,  Vol.  XXIV,  pages  104-107  and  page  120,  August  4  and  n, 
1894- 

J  Transactions  American  Institute  of  Electrical  Engineers,  Vol.  XXVIII,  page 
1482,  December,  1909. 


COSTS   AND   SELLING   PRICE.  13 

per  kilowatt-hour,  the  ordinates  of  curve  C  show  the  fixed 
charge  (interest  at  5  per  cent.,  taxes  and  administrative 
expenses  I  per  cent.,  and  depreciation  5  per  cent.)  per  kilowatt- 
hour,  and  the  ordinates  o.f  curve  D  show  the  total  cost  per 
kilowatt-hour.  Thus  at  100  per  cent,  load  factor  the  cost  is 


60        „     8O  100  120  140 

percent  load 

Fig.  8. 

half-a-cent  per  kilowatt-hour,  and  at  20  per  cent,  load  factor 
the  cost  is  0.97  cent  per  kilowatt-hour  at  the  switchboard. 

Multiplying  the  tabulated  costs  in  the  above  table  by  the 
corresponding  values  of  the  load  factor,  one  can  see  the  extent 
to  which  the  various  items  of  total  cost  change  with  the  load 
on  the  station,  as  estimated  by  B.  J.  Arnold.  Similarly  the 
ordinates  of  the  various  curves  in  Fig.  8  may  be  multiplied  by 
"per  cent,  load"  to  give  the  various  items  of  total  cost  at  dif- 
ferent station  loads  as  estimated  by  H.  G.  Stott. 

5.  Cost  of  electrical  energy  delivered  to  the  consumer. — The 
foregoing  articles  discuss  the  cost  of  electrical  energy  at  the 
switchboard.  The  cost  of  electrical  energy  delivered  to  the 


14  ELECTRIC    LIGHTING. 

consumer  is  greater  than  the  cost  at  the  switchboard  by  an 
amount  sufficient  to  cover  the  following  items:  (a)  The  interest 
on  the  cost,  and  depreciation  of  the  distributing  system ;  (b)  the 
energy  lost  in  the  distributing  system ;  (c)  the  interest  on  the 
cost  of  meters,  and  depreciation  and  repair  of  the  meters;  and 
(d)  the  cost  of  reading  meters,  making  out  bills  and  collecting 
same. 

The  cost  of  the  distributing  system  varies  so  greatly  with  local 
conditions  that  it  is  impossible  to  give  any  general  estimate. 
The  cost  is  especially  great  where  the  consumers  are  scattered 
over  a  large  district,  or  where  costly  underground  distributing 
cables  are  used;  and  the  cost  varies  greatly  with  the  system  of 
distribution  employed.  Thus  high -voltage  alternating-current 
distribution  with  step-down  transformation  is  much  cheaper 
than  low-voltage  direct-current  distribution  when  the  consumers 
are  widely  scattered. 

Complete  statistics  of  a  small  municipal  electric  lighting  plant 
are  given  in  Art.  15,  and  some  idea  of  the  difference  between  cost 
of  electrical  energy  at  switchboard  and  Cost  delivered  to  the 
consumer  may  be  obtained  by  comparing  these  statistics  with 
the  cost  statistics  which  are  given  in  Art.  3. 

6.  Customer's  load  factors.  The  diversity  factor.*— The  aver- 
age power  delivered  to  a  customer  divided  by  his  maximum  de- 
mand is  called  his  load  factor.  Thus  the  general  average  of  24, 1 77 
small  living  apartments  in  Chicago  was  18.34  kilowatt-hours 
monthly  consumption  (representing  an  average  continuous  con- 
sumption of  25.5  watts  per  customer)  and  an  average  maximum 
demand  of  370  watts  per  customer,  so  that  the  average  load 
factor  of  these  customers  was  0.069. 

If  the  load  factor  of  an  electric  lighting  station  were  as  low  as 

*  See  a  paper  by  H.  G.  Gear,  Transactions  American  Institute  of  Electrical  En- 
gineers, Vol.  XXIX,  pages  375~384.  March  1910.  The  examples  of  customer's 
load  factors  which  are  given  in  the  text  are  taken  from  this  paper. 

See  also  a  paper  which  was  read  by  Mr.  E.  W.  Lloyd  before  the  Atlantic  City 
Convention  of  the  National  Electric  Light  Association,  June,  1909.  The  curves 
of  Fig.  9  are  taken  from  this  paper. 


COSTS   AND   SELLING   PRICE.  15 

0.069  the  cost  of  electric  lighting  would  be  almost  prohibitive, 
but  the  load  factor  of  a  station  is  always  very  much  larger  than 
the  average  load  factor* of  the  customers,  because  the  maximum 
demands  of  the  customers  never  come  at  the  same  time.  This 
diversity  among  the  customers  is  a  very  important  element  in  the 
cost  of  electric  lighting. 

The  combined  actual  maximum  demand  of  a  group  of  cus- 
tomers divided  by  the  sum  of  their  individual  maximum  demands 
is  called  their  diversity  factor.  The  diversity  factor  is  here  defined 
with  respect  to  a  group  of  customers  but  it  can  also  be  applied  to 
a  group  of  lamps  or  a  group  of  feeders  as  shown  in  the  following 
examples. 

Diversity  factor  of  a  customer's  group  of  lamps. — A  customer 
has  fifty  5O-watt  lamps  and  of  course  the  sum  of  the  individual 
maximum  demands  of  the  lamps  is  2,500  watts  ("connected 
load").  The  customer's  maximum  demand,  however,  is  1.5 
kilowatts.  Therefore  the  diversity  factor*  of  the  customer's 
group  of  lamps  is  0.60.  The  ordinates  of  the  curves  in  Fig.  9 


I 

1, 

P 

5 

c 

maximum  divided  by  connected  lo 

W  4»  tn  O*  *J  CO  ^ 

1 

i 

! 

Q 

1 

n 

B 

i  ,• 

\ 

V 

1 

JS 

4\ 

* 

d 

I 

§ 

V 

\ 

>C 

—^ 

•^~— 

-\ 

c 

\ 

\ 

\ 

> 

*^ 

/ 

V-C 

s 

B 

~^r< 

L. 

V- 

/' 

\ 

s 

-- 

-— 

-^ 

^ 

<- 

^ 

X 

A 

__ 

^ 

\ 

, 

10    20    30    40    50    60    7° 

o    90    10 

number  of  50-watt  lamps    connected 

Fig.  9.     Curve  A  average  of  30,729  residences.     Curve  B  average  of  5,392  offices. 

Curve  C  average  of  9,149  small  stores. 

*  The  diversity  factor  of  a  customer's  group  of  lamps,  namely,  the  ratio  of  maxi- 
mum demand  to  connected  load  is  usually  called  the  demand  factor  of  the  customer. 


16  ELECTRIC    LIGHTING. 

show  the  ratio  maximum  demand  to  connected  load  for  various 
kinds  of  electric  lighting  service  in  Chicago. 

Diversity  factor  of  a  group  of  customers. — The  sum  of  the 
individual  maximum  demands  of  the  various  customers  in 
a  densely  populated  residence  block  in  Chicago  was  63  kilowatts, 
whereas  the  maximum  demand  upon  the  service  transformer 
which  supplies  the  block  was  18  kilowatts.  Therefore  the  diver- 
sity factor  of  the  group  of  customers  was  0.286. 

Diversity  factor  of  a  number  of  feeders. — The  actual  maxi- 
mum demand  upon  a  particular  substation  in  Chicago  was  1,000 
kilowatts,  and  the  sum  of  the  maximum  loads  on. the  10  sets 
of  feeders  which  go  out  from  the  substation  was  1 ,200  kilowatts. 
The  diversity  factor  of  the  group  of  feeders  was  therefore  0.833. 

7.  Analysis  of  costs  of  electric  service.* — There  are  three  fairly 
distinct  items  of  cost  of  a  customer  to  a  central  station,  and 
any  equitable  schedule  of  rates  for  electric  service  should  be 
based  on  a  careful  consideration  of  these  costs  which  are  as 
follows : 

(a)  Connection  cost. — A  certain  service  is  rendered  to  a  cus- 
tomer in  that  power  from  a  central  station  is  available  for  his 
use  at  all  times  even  if  he  does  not  actually  make  use  of  it. 
This  service  of  the  central  station  is  usually  called  "readiness 
to  serve"  and  its  cost  to  the  central  station  includes  a  small 
part  of  the  total  annual  expense  of  the  entire  plant  and  distrib- 
uting system.  It  includes  a  large  part  of  the  interest  on  the 
cost  of  the  customer's  wiring  connections  and  meter;  and  it 
includes  a  large  part  of  the  cost  of  maintaining  and  reading 

*  This  matter  is  discussed  at  some  length  in  the  following  papers:  "Central 
Station  Charging  Systems  in  Use  in  the  United  States,"  Electrical  World  and 
Engineer,  Vol.  XL,  pages  361-366,  September  6,  1902.  "Methods  of  Charging 
for  Electrical  Energy,"  E.  H.  Crapper,  Electrician  (London),  Vol.  HI,  pages 
330-332,  December  18,  1903.  "Method  of  Charging  for  Electrical  Energy," 
Schofiborn,  Electrotechnische  Zeitschrift,  Vol.  XXV,  pages  377-378,  May  12,  1904. 
"Price  of  Electricity,"  by  R.  S.  Hale,  Superintendent  Sales  Department,  Boston 
Edison  Company.  This  paper  was  read  before  the  New  England  Section  of  the 
National  Electric  Light  Association  on  March  16,  1910. 


COSTS   AND    SELLING    PRICE.  17 

his  meter,  and  a  portion  of  the  cost  of  the  station  book-keeping. 
The  cost  to  the  central  station  of  "readiness  to  serve"  is  called 
connection  cost. 

(b)  Demand  cost. — A  certain  service  is  rendered  to  a  customer 
because  of  and  in  proportion  to  his  maximum  demand  for  power. 
The  cost  of  this  service  to  the  central  station  is  called  the  cus- 
tomer's demand  cost.     The  size  of  a  station  (and  therefore  the 
total  investment)  is  determined  by  the  total  maximum  demand 
for  power,  and  therefore  interest  on  investment,  taxes,  and  a 
portion  of  the  depreciation  should  be  distributed  among  the 
various  customers  as  a  demand  charge;  but  a  customer  who 
never  uses  power  at  the  time  of  heavy  load  (on  the  peak)  may 
pay  little  or  nothing  for  demand. 

(c)  Consumption   cost. — A   certain   service   is   rendered   to   a 
customer  because  of  and  in  proportion  to  his  total  energy  con- 
sumption in  kilowatt-hours,  and  the  cost  of  this  service  to  the 
central  station  is  called  the  customer's  consumption  cost.     The 
total    consumption    cost   of   all    the    customers  of   a  station  is 
approximately  equal  to  the  cost  of  coal  plus  the  cost  of  labor  and 
station  supplies. 

A  careful  analysis  of  service  costs  (electric  lighting)  has  been 
made  by  Mr.  S.  E.  Doane*  upon  the  basis  of  very  full  statistics 
of  112  central  stations  in  the  United  States,  and  the  results 
are  shown  in  the  following  table. 

*  "High  Efficiency  Lamps  and  their  Effect  on  the  Cost  of  Light  to  the  Central 
Station,"  a  paper  read  before  the  St.  Louis  convention  of  the  National  Electric 
Light  Association,  May,  1910. 

A  very  important  source  of  information  in  matters  of  operation  costs  and  the 
fixing  of  rates  for  electrical  service  is  the  series  of  Annual  Reports  of  the  Massa- 
chusetts Commissioners  of  Gas  and  Electric  Light. 

The  Railway  Commission  of  Wisconsin  has  made  a  most  exhaustive  study  of 
the  costs  of  electric  service  in  their  handling  of  the  celebrated  case  of  The  State 
Journal  Printing  Company  vs.  The  Madison  Gas  and  Electric  Company.  The 
decision  of  the  Commission  was  rendered  March  8,  1910,  and  copies  of  it  may  be 
obtained  by  addressing  the  commission.  The  decision  is  discussed  in  some  detail 
by  Mr.  Percy.  H.  Thomas  in  the  Electrical  Journal,  Vol.  VII,  pages  560-574,  July, 
1910. 


18 


ELECTRIC    LIGHTING. 


Average  of  40 
Small  Stations 
in  the  West. 
Per  Cent. 

Average  of  70 
Small  Stations 
in  the  East. 
Per  Cent. 

One  Large  Station 
Giving  Free 
Lamp  Renewals. 
Per  Cent. 

Another  Large  Sta- 
tion Giving  Free 
Lamp  Renewals. 
Per  Cent. 

Connection  cost  . 
Demand  cost.  .  .  . 
Consumption  cost 

II-S 
59-6 
28.9 

II-3 
50.8 
37-9 

18.0 
58.5 
23-5 

17.7 

55-1 
27.2 

Total  

IOO.O 

IOO.O 

IOO.O 

IOO.O 

8.  The  fixing  of  rates  for  electric  service.* — Inasmuch  as  the 
cost  of  electrical  service  may  be  resolved  into  connection  cost, 
demand  cost,  and  consumption  cost,  therefore  the  rational 
method  of  charging  for  the  service  would  be  to  separate  the  charge 
into  three  items,  namely,  (a)  a  fixed  charge  per  year  to  cover 
connection  cost,  (6)  a  yearly  charge  per  kilowatt  of  maximum 
demand,  and  (c)  a  charge  of  so  much  per  kilowatt-hour  of  con- 
sumption. Each  of  these  items  should  exceed  the  correspond- 
ing cost  so  as  to  give  a  fair  margin  of  profit. 

In  establishing  a  schedule  of  rates,  however,  a  number  of 
things  must  be  carefully  considered,  some  of  which  are  as  follows: 
(i)  There  is  a  strong  popular  prejudice  against  a  fixed  charge 
(connection  charge),  and  therefore  this  item  is  seldom  or  never 
included  in  price  schedules;  (2)  the  price  schedule  must  be 
arranged  to  attract  business  by  setting  a  low  price  (low  margin 
of  profit)  on  business  that  is  open  to  sharp  competition;  and 
(3)  a  simple  price  schedule  is  a  practical  necessity.  There 
are  three  more  or  less  distinct  price  schedules  used  by  every 
central  station  as  follows: 

(a)  For  small  residence  lighting.     A  certain  fairly  high  rate, 
usually  II  to  15  cents  per  killowatt-hour,  for  energy  consump- 
tion with  a  minimum  charge  which  is  usually  $1.00  per  month. 

(b)  For  large   consumers  whose   maximum  demands  are  on 
the  peak.     A  charge  of,  say,  $60.00  per  year  for  each  kilowatt 

*  A  very  good  discussion  of  rates  is  given  by  R.  S.  Hale  in  the  General  Electric 
Review,  Vol.  XIV,  pages  157-169,  April,  1911.  The  student  is  likely  to  get  an 
altogether  erroneous  idea  of  rate  making  from  the  foregoing  analysis  of  costs 
because  the  employment  of  averages  tends  to  obscure  the  fact  that  there  is  an  endless 
variety  of  conditions  to  be  met  with  in  electric  service.  The  reading  of  Mr.  Hale's 
article  is  strongly  recommended. 


COSTS   AND   SELLING   PRICE.  19 

of  maximum  demand,  and  a  low  rate,  say  2  or  3  cents  per  kilo- 
watt-hour, for  energy  consumption. 

(c)  For  operating  motors  off  the  peak.  A  consumption 
charge  of  3  to  8  cents  per  kilowatt-hour. 

Equitable  charges  for  electric  service  may  be  realized  by 
resolving  the  service  into  its  cost  elements  ("connection," 
"demand"  and  "consumption")  and  charging  all  classes  of 
customers  at  the  same  rate  for  each  element;  or  the  customers 
may  be  carefully  classified  on  the  basis  of  their  "connection," 
"demand"  and  "consumption"  costs,  and  a  certain  equitable 
rate  per  kilowatt-hour  of  consumption  may  be  set  for  each  class. 
The  following  table  illustrates  the  complete  equivalence  of 
the  two  systems  of  charging. 


Class  of  Service. 

Connected  Load 
Expressed  in 
5o-watt  Units. 

Connection 
Charge,  Dollars 
per  Month. 

Maximum  Demand  in 
Kilowatts. 

A.  Domestic  (small)  .  . 
B.  Domestic  (medium) 
C.  Domestic  (large)   .  . 
D.  Store  lighting  
E.  Small  factory  light- 
ing 

IO 
2O 
50 
80 

80 

ioo  (5  H.P.) 

0.50 

0-75 

I.2S 
1.50 

1.50 
i-75 

0.35  at  peak 
0.50  at  peak 
i.  oo  at  peak 
4.00  at  peak 

4.00  off  peak 
5.00  off  peak 

F.  Motor  driving  

Class  of  Service. 

Desani?Paer  vTisAr^e 
&«  cf  l°pS,n 

watt  on  Peak.      Kilowatt-hours. 

Consumption 
Charge.  Dollars 
per  Month,  at  3 
Cents  per 
Kilowatt-hour. 

Total 
Monthly 
Charge  in 
Dollars. 

Equivalent 
Class  Rate  in 
Cents  per 
Kilowatt-hour. 

^ 
B. 

%. 
| 

1-65                    IS 
2-50                   35 
5.00                   80 
20.00                 360 
240 
900 

0-45 
I.OS 
2.40 
10.80 
7.2O 
27.00 

2.6o 
4-30 
8.65 
22.30 
8.70 
28.75 

17-3 
12.3 
10.8 

6.2 

3-6 
3-2 

An  objection  .to  the  charging  for  electrical  service  by  the 
kilowatt-hour  of  consumption  (using  classified  rates)  is  that 
it  places  a  false  premium  on  the  economical  use  of  current  by 
the  customer.  Thus  a  customer  might  reduce  his  monthly 
bill  to  one-half  by  reducing  his  killowatt-hour  consumption  to 
one-half,  whereas  his  cost  to  the  central  station  would  be  reduced 


20  ELECTRIC    LIGHTING. 

but  very  little  if  his  maximum  demand  is  not  reduced  in  pro- 
portion to  his  kilowatt-hour  consumption.  The  time  of  day 
when  a  customer  economizes  is  very  important  to  the  central 
station. 

Another  objection  (which  applies  during  a  time  when  an  im- 
proved high-efficiency  lamp  like  the  tungsten  lamp  is  being 
introduced)  is  that  a  customer  can  reduce  his  kilowatt-hour 
consumption  to,  say,  one-third  for  the  same  amount  of  light, 
and  thus  reduce  his  monthly  bill  to  one- third;  whereas  his  cost 
to  the  central  station  will  not  be  reduced  in  the  same  proportion. 
In  fact  the  advent  of  the  tungsten  lamp  has  brought  the  whole 
question  of  electric  service  costs  into  a  prominence  which  it 
has  not  had  for  years. 

9.  The  meter-rate  system  and  the  flat-rate  system  for  sell- 
ing electrical  service. — A  central  power  station  supplies  energy 
to  its  customers  and  it  may,  therefore,  seem  that  the  use  of  an 
energy  meter  (a  watt-hour-meter)  would,  like  the  use  of  a  gas 
meter,  furnish  a  complete  and  equitable  basis  for  charging  cus- 
tomers, but  it  is  not  so.  In  supplying  gas  for  lighting,  the  large 
storage  reservoir  makes  the  gas  generating  plant  independent 
of  the  irregular  consumption  of  the  gas.  In  an  electric  plant, 
on  the  other  hand,  electrical  energy  must  be  generated  as  used, 
except  in  the  few  cases  where  storage  batteries  can  be  economi- 
cally employed,  and,  therefore,  the  capacity  of  the  electric  plant 
must  be  sufficient  to  meet  the  maximum  demand  for  power. 
This  matter  is  discussed  in  detail  in  Articles  5  to  8.  The  selling 
of  electrical  energy  by  the  kilowatt-hour  as  indicated  by  the 
watt-hour  meter  is  called  the  meter-rate  system. 

In  the  early  days  of  electric  lighting  the  customer  paid  so 
much  per  month  for  each  lamp  installed.  This  method  of 
selling  electrical  service  is  called  the  flat-rate  system.  The  flat- 
rate  system  is  more  satisfactory  than  the  meter-rate  system  be- 
cause it  simplifies  the  station  book-keeping  and  avoids  the  cost 
of  installing,  maintaining  and  reading  of  meters,  and  it  avoids 


COSTS    AND    SELLING    PRICE.  21 

the  consumption  of  energy  in  the  meter.  On  the  other  hand, 
the  flat-rate  system  i^  unsatisfactory  because  under  this  system 
a  wasteful  customer  pays  no  more  than  an  economical  one,  and 
a  dishonest  customer  can  connect  lamps  in  excess  of  the  number 
he  pays  for.  These  two  disadvantages  of  the  flat-rate  system 
may,  however,  be  overcome  to  some  extent  as  follows:  In  the 
first  place  if  the  customer  uses  high-efficiency  tungsten  lamps  the 
cost  of  the  lamps  themselves  is  an  incentive  to  short  hours  of 
use ;  and  in  the  second  place  the  so-called  excess  indicator  can  be 
used  to  limit  the  amount  of  power  delivered  to  the  customer. 
The  excess  indicator  is  a  device  essentially  like  an  ordinary  bell 
or  buzzer;  the  current  which  is  delivered  to  a  customer  flows 
through  the  winding  of  an  electromagnet  and  when  the  customer 
turns  on  more  than  a  prescribed  number  of  lamps  the  armature  of 
the  electro-magnet  is  attracted  and  the  circuit  is  interrupted 
repeatedly,  causing  the  lights  to  flicker  in  a  manner  which  makes 
them  practically  useless.  The  excess  indicator  is  much  cheaper 
than  a  watt-hour  meter  and  it  needs  less  attention.  Without 
doubt  the  extension  of  electrical  service  to  great  numbers  of  very 
small  customers  is  hampered  by  the  prevailing  idea  that  the 
meter-rate  system  must  be  used,  and  the  cost  of  installing,  main- 
taining and  reading  meters  is  probihitive  in  the  case  of  a  very 
small  customer.  The  very  small  customer  should  be  supplied 
on  the  flat-rate  system  buying  his  own  tungsten  lamps  and  using 
them  under  the  control  of  an  excess  indicator. 

10.  The  watt-hour  meter*  is  a  device  for  summing  up  the 
total  amount  of  work  or  energy  delivered  to  a  circuit.  This 
meter  is  sometimes  used  on  a  station  switchboard  to  measure  the 
energy  output  of  the  station.  Thus  the  annual  output  of  the 
Wallingford  station  (464,000  kilowatt-hours,  see  page  32)  was 

*  A  good  description  of  the  various  types  of  watt-hour  meter  is  given  in  The 
Watt-hour  Meter,  by  Shepard  and  Jones,  Technical  Publishing  Company,  San  Fran- 
cisco, California,  1910.  This  book  also  contains  information  relating  to  the  main- 
tenance of  the  meter  department  of  an  electric  power  station. 

Everyone  who  has  to  do  with  watt-hour  meters  should  possess  a  copy  of  the 
Meter  Code  of  the  National  Electric  Light  Association. 


22  ELECTRIC    LIGHTING. 

measured  by  a  watt-hour  meter  in  the  station.  The  watt-hour 
meter  is  chiefly  used,  however,  to  measure  the  energy  delivered 
to  a  customer. 

In  the  following  discussion  of  the  two  most  important  types  of 
watt-hour  meter  (the  commutator-motor  type  and  the  induction- 
motor  type),  it  is  shown  that  the  speed  of  the  motor  spindle  is 
proportional  to  the  watts  delivered  to  the  receiving  circuit;  that 
is  to  say,  the  rate  at  which  the  spindle  turns  is  proportional  to  the 
rate  at  which  energy  is  delivered  to  the  receiving  circuit;  therefore* 
the  total  angle  (or  number  of  revolutions)  turned  by  the  spindle 
is  proportional  to  the  total  energy  delivered,  and  a  revolution 
counter  may  be  arranged  to  indicate  the  delivered  energy  in 
kilowatt-hours. 

ii.  The  Thomson  watt-hour  meter  is  a  small  electric  motor 
of  the  commutator  type  (without  iron)  driving  a  revolution 
counter.  The  field  coils  BB,  Fig.  10,  are  made  of  coarse  wire 
and  they  are  connected  in  series  with  the  receiving  circuit  or 
"load"  so  that  the  total  current,  i,  which  is  delivered  to  the 
receiving  circuit  flows  through  the  field  coils  The  armature  A 
is  wound  with  fine  wire  and  it  is  connected  across  the  supply 
mains  in  series  with  a  non-inductive  resistance  R  so  that  a 
current  equal  to  e/R  flows  through  the  armature,  e  being  the 
voltage  between  the  mains.  The  brushes  dd  are  made  of  metal 
and  they  rub  very  lightly  on  a  small  commutator  e.  This  com- 
mutator has  silver  bars  so  as  to  give  good  electrical  connection 
with  a  minimum  of  friction.  The  armature  is  mounted  on  a 
vertical  spindle  which  rests  on  a  jewel  so  as  to  turn  with  as  little 
friction  as  possible,  and  the  opposition  to  rotation  is  due  to  the 

*  This  simple  case  of  integration  occurs  frequently  in  mathematical  arguments, 
and  it  should  be  understood  perfectly  by  the  student.  Thus  the  rate  of  change 
of  one  quantity  y  is  proportional  to  the  rate  of  change  of  another  quantity  x\ 
that  is  to  say,  the  rate  of  change  of  y  is  k  times  as  great  as  the  rate  of  change  of 
x.  Therefore,  if  y  and  x  start  from  zero  together,  y  must  be  always  k  times 
as  large  as  x.  If  one  person  A  saves  money  10  times  as  fast  as  another  person 
B,  then  A  will  always  have  ten  times  as  much  as  B  if  A  and  B  start  from  zero 
together. 


COSTS    AND    SELLING    PRICE. 


electromagnetic  drag  of  the  permanent  magnets  MM  upon  the 
copper  disk  /  which  is  attached  to  the  spindle.  The  result  is 
that  the  speed  of  the  armature  and  spindle  is  almost  exactly 
proportional  to  the  driving  torque  which  is  exerted  on  the 


Fig.  10. 

armature  A  by  the  field  coils  BB,  and  this  driving  torque  is 
proportional  to  the  product  of  field  current  i  and  armature 
current  e/R.  Therefore  the  speed  is  proportional  to  ei  (watts 
delivered  to  the  receiving  circuit). 

The  commutator-motor  type  of  watt-hour  meter  can  be  used 
on  direct-current  or  alternating-current  circuits. 

The  compensation  for  friction  in  the  Thomson  meter. — An  auxiliary  fine-wire 
field  coil  connected  in  series  with  the  armature  is  always  provided  in  the  Thomson 
meter.  The  effect  of  this  coil  is  to  give  a  constant  driving  torque  (supply  voltage 
assumed  to  be  constant)  sufficient  to  overcome  friction.  This  auxiliary  field  coil 
is  called  a  starting  coil  and  it  gives  a  great  increase  of  accuracy  of  the  meter. 

12.  The  induction  watt-hour  meter  is  a  small  induction 
motor  driving  a  revolution  counter,  and  it  can  be  used  only  on 
alternating-current  circuits.  The  essential  features  of  the  motor 
part  of  the  meter  are  shown  in  Fig.  n.  A  thin  disk  DD  of 
aluminum  or  copper  is  mounted  on  a  spindle  and  rotates  in  front 


24 


ELECTRIC    LIGHTING. 


of  the  three  lugs  BAB  of  a  laminated  iron  structure  as  shown. 
The  lugs  BB  are  wound  with  coarse  wire  and  this  winding  (the 
current  winding)  is  connected  in  series  with  the  receiving  circuit 
so  that  the  current  i  which  is  delivered  to  the  receiving  circuit 
flows  through  the  windings  on  BB.  The  magnetic  field  in  front 
of  the  lugs  BB  is  therefore  proportional  to  i.  The  lug  A  is 
wound  with  fine  copper  wire  and  this  winding  (the  voltage  winding} 


L  'li  \\Laminaied  iron\'  illl,  ''li 
"  'liH'!'  .li'W.li'.ll'.ll'lli  ll 


Fig.   11. 

is  connected  directly  across  the  supply  mains.  If  the  resistance 
of  the  winding  on  A  is  negligible,*  then  the  alternating  magnetic 
flux  through  the  lug  A  induces  a  voltage  in  the  winding  A  which 
balances  (and  is  therefore  equal  to)  the  supply  voltage  e,  and 
this  alternating  flux  induces  a  proportional  voltage  (proportional 


*  Negligible  in  comparison  with  the  very  large  reactance  of  the  coil.     It  is  not 
wholly  negligible.     See  discussion  of  compensation  for  lag. 


COSTS   AND    SELLING    PRICE. 


to  e)  along  the  dotted  lines  in  the  disk  (around  the  bundle  of  flux 
which  passes  through  the  disk).  This  voltage  in  the  disk  pro- 
duces a  current  in  the  disk  which  is  proportional  to  it  and  to  e 
(disk  assumed  to  be  non-inductive),  and  this  current  as  it  flows 
under  the  lugs  BB  is  pushed  s  dewise  by  the  flux  with  a  force 
which  is  proportional  to  the  current  in  the  disk  and  to  the  flux 
density  under  the  lugs  BB.  But  the  current  in  the  disk  is 
proportional  to  e,  and  the  flux  density  under  BB  is  proportional 
to  i,  therefore  a  driving  torque  proportional  to  ei  is  exerted  on 
the  disk.* 

The  meter  spindle  carries  a  copper  diskf  similar  to  /  in  Fig. 
10,  which  rotates  between  the  poles  of  permanent  magnets  like 
MM,  Fig.  10,  and  therefore  the  speed  of  the  meter  is  proportional 
to  ei,  as  in  the  Thomson  meter. 

Compensation  for  friction  and  lag  in  the  induction  meter.  { — If  the  driving  torque 
of  the  induction  meter  were  Strictly  proportional  to  the  delivered  watts,  the  speed 
of  the  meter  spindle  would  not  be 
proportional  to  delivered  watts 
because  of  friction.  The  effect  of 
friction  may  be  to  a  great  extent 
eliminated,  however,  by  means  of 
a  device  whereby  the  voltage 
winding  (on  lug  A,  Fig.  n)  alone 
produces  an  amount  of  torque 
sufficient  to  overcome  friction. 
This  is  usually  done  by  placing  a 
flat  short-circuited  coil  5  between 
the  lug  A  and  the  disk  DD,  as 
shown  in  Fig.  12,  and  adjusting  this 
coil  sidewise  until  the  desired  torque 


D 


voltage  coil 


direction  of 
motion  of  disk 


is    produced   by  the  voltage    coil.  Fig.   12. 

The  coil,  5,  is  called  a  shading  coil. 

In  order  that  the  combined  action  of  lugs  A  and  B,  Fig.  n,  may  produce 
a  driving  torque  which  is  accurately  proportional  to  the  delivered  watts,  the  voltage 
induced  in  the  disk  by  the  magnetic  flux  from  lug  A  must  produce  a  current  in 

*  The  flux  from  lugs  B  also  induces  currents  in  the  disk,  these  currents  flow 
across  the  face  of  lug  A,  and  the  flux  under  lug  A  pushes  widewise  on  these 
currents.  It  can  be  easily  shown  that  this  torque  is  also  proportional  to  ei. 

t  Usually  the  disk  DD,  Fig.  n,  serves  also  as  the  damping  disk. 

%  Full  details  of  the  compensation  of  the  induction  meter  may  be  found  on  pages 
28-38  of  Shepard  and  Jones'  The  Watt-hour  Meter. 


26  ELECTRIC   LIGHTING. 

the  disk  which  is  in  phase  with  the  voltage  across  the  mains.  In  fact,  however, 
the  current  in  the  disk  is  not  in  phase  with  the  supply  voltage  for  two  reasons: 
(i)  The  voltage  winding  does  not  have  a  negligible  resistance,  and  (2)  The  current 
paths  in  the  disk  are  not  non-inductive.  The  error  due  to  this  effect  is  especially 
noticeable  when  the  meter  is  used  to  measure  energy  delivered  to  a  receiving  circuit 
of  low  power  factor,  and  this  error  may  be  to  a  great  extent  eliminated  by  means 
of  an  auxiliary  secondary  coil  L  on  lug  A,  as  shown  in  Fig.  12,  this  coil  being 
short  circuited  through  an  adjustable  resistance  R.  This  auxiliary  coil  con- 
stitutes what  is  called  the  lag  adjustment  of  the  meter.* 

13.  The    two-rate    meter. — One    of    the    most    satisfactory 
schemes  for  selling  electrical  service  is  to  charge  at  a  high  rate 
per  kilowatt-hour  during  the  period  of  heavy  station  load  (on 
the  peak)  and  to  charge  at  a  low  rate  per  kilowatt-hour  during 
the  period  of  light  station  load  (off  the  peak).     To  carry  this 
scheme  into  effect  requires  the  use  of  the  two-rate  meter  which  is 
an  ordinary  watt-hour  meter  with  two  sets  of  dials  and  a  clock 
which  throws  into  gear  one  set  of  dials  during  the  period  of  heavy 
station  load  (between  7  and  10  P.M.,  for  example)  and  the  other 
set  of  dials  during  the  remainder  of  the  24  hours  of  each  day. 
One  set  of  dials  thus  registers  the  kilowatt-hours  of  consumption 
on  the  peak  and  the  other  set  of  dials  registers  the  kilowatt-hours 
of  consumption  off  the  peak.     The  practical  objection  to  the 
two-rate  meter  is  that  a  high  grade  and  expensive  clock  is  re- 
quired in  order  that  the  clock  may  run  for  a  month  without  too 
great  an  error. 

14.  The  maximum-demand  meter,  f — The  system  of  selling 
electrical  service  in  which  a  certain  charge  per  year  is  made  for 
each  kilowatt  of  maximum  demand  and  a  certain  charge  per 
kilowatt-hour  of  consumption,  requires  the  use  of  two  distinct 
meters,  namely,  a  maximum-demand  meter  and  a  watt-hour 
meter.     The  most  extensively  used  maximum-demand  meter  is 
the  Wright  meter,  which  is  essentially  a  large  thermometer,  the 
bulb  of  which  is  heated  by  a  low-resistance  strip  of  metal  through 
which  the  current  demanded  by  the  customer  flows.     A  mo- 

*  The  theory  of  the  lag  adjustment  of  the  induction  watt-hour  meter  is  fully 
explained  on  pages  28-33  °f  Shepard  and  Jones'  The  Watt-hour  Meter. 
f  See  Shepard  and  Jones'  The  Watt-hour  Meter,  pages  100-105. 


COSTS   AND    SELLING    PRICE.  27 

mentary  short  circuit  does  not  heat  the  bulb  of  the  thermometer 
perceptibly,  but  a  heavy  demand  lasting  for  five  or  six  minutes 
heats  the  bulb  up  to*  a  certain  temperature,  a  portion  of  the 
liquid  in  the  bulb  flows  over  into  a  graduated  trap,  and  the 
maximum  demand  for  current  is  indicated  by  the  amount  of 
liquid  in  this  trap.  After  reading,  the  instrument  is  tilted  so  as 
to  cause  the  liquid  in  the  trap  to  flow  back  into  the  bulb. 

The  maximum-demand  meter  is  not  as  yet  extensively  used. 
A  central  station  using  a  schedule  of  rates  which  involves  a 
yearly  charge  for  maximum  demand*  may  estimate  the  maximum 
demands  of  its  customers  on  the  basis  of  statistics  such  as  are 
represented  in  Fig.  9. 

15.  The  Borough  Electric  Plant  of  Wallingford,  Connecti- 
cut.!— The  cost  of  erection  of  this  plant  was  met  by  the  pro- 
ceeds ($56,500.00)  from  the  sale  of  2O-year  municipal  bonds  bear- 
ing interest  at  3^2  Per  cent.,  the  face  value  of  the  bonds  being 
$55,000.00.  The  plant  began  operating  on  December  23,  1899. 
The  station  building  is  of  brick  and  steel  construction,  45  feet  X 
104  feet.  At  the  beginning  the  plant  included  the  necessary 
boilers,  a  1 5O-horse-power  eng  ne  belted  to  a  75-kilowatt  alter- 
nator, a  225-horse-power  engine  belted  to  a  i5O-kilowatt  alter- 
nator, the  necessary  switchboards  and  accessory  apparatus, 
including  three  constant-current  transformers  for  operating  three 
arc-lamp  circuits  for  street  lighting,  and  a  distributing  system 
for  commercial  lighting. 

A  45O-horse-power  engine  and  a  24O-kilowatt,  2-phase  alter- 
nator with  additional  boilers  were  installed  in  1904.  A  small 
water-power  plant  with  a  generator  capacity  of  120  kilowatts 
was  installed  in  1907.  The  distributing  system  (pole  lines  and 
transformers)  has  been  slowly  extended  year  by  year  as  roughly 
indicated  by  the  yearly  increase  of  the  number  of  customers  (see 
Fig.  14,  curve  G). 

*  See  Art.  8. 

t  A  series  of  detailed  annual  reports  of  this  plant  and  the  kind  permission  of  the 
manager.  Mr.  A.  L.  Pierce,  to  use  them  here  makes  it  possible  to  give  a  good  example 
of  the  economies  of  a  small  lighting  plant. 


28 


ELECTRIC    LIGHTING. 


In  1906  about  45  kilowatts  of  power  were  expended  for  operat- 
ing the  street  lamps  (89  enclosed-arc  lamps  and  eight  loo-watt 
incandescent  lamps).  In  1907  fifty-eight  incandescent  lamps 
(carbon  filament)  and  one  enclosed-arc  lamp  were  added  to  the 
street  lighting  system  which  was  extended  to  an  adjoining  village, 
and  the  total  power  expended  for  street  lighting  was  about  50 

140 


100 


80 


60 


40 


20 


£ 

V 

At 

Y 

; 

/ 

H 

/ 

7 

E 

| 

/ 

? 

"fc 

K 

1 

At 

p* 

Ir 

--^ 

<M 

plant  \ 

tega 

n  operation 

\ 

j 

Dece 

mbe 

r23, 

186 

9 

B 

Y 

Y 

^ 

^ 

^ 

Y^ 

r-" 

B* 

)  —  < 

r^ 

1900       1902        1904       1906       1908       1910 
August  1 

Fig.  13.     Curve   A  assets.     Curve  B   accumulated  depreciation. 

kilowatts.  In  1910,  all  but  9  of  the  enclosed-arc  lamps  and  all 
of  the  carbon-filament  lamps  were  replaced  by  tungsten  lamps, 
and  the  power  consumed  for  lighting  was  about  40  kilowatts. 

The  plant  was  operated  only  at  night  (about  14  hours  per 
day)  until  1908,  when  it  was  operated  about  1 8  hours  per  day 
and  in  1909  a  continuous  day  and  night  service  was  begun. 

The  population  of  Wallingford  was  about  7,000  in  1900,  and 
about  5,000  inhabitants  were  included  within  the  service  area  of 
the  plant.  In  1910  the  distributing  system  had  been  extended 


COSTS   AND    SELLING   PRICE. 


29 


to  include  the  adjoining  villages  of  Yalesville  and  Tracy  and 
about  10,000  inhabitants  were  included  in  the  service  area  of  the 
plant. 

The  entire  capital  invested  in  the  plant  has  grown  out  of  the 
proceeds  of  the  bonds  above  mentioned,  and  the  net  assets  of 


"§2 

a 

•c 


A 


G 


'» 


U. 


10 


1901 


1903 


1905 


1907 


1909 


1911 


Fig.  14.  Curve  C  capacity  of  plant.  Curve  D  connected  lighting  load. 
Curve  E  connected  load  of  motors  and  heating  apparatus.  Curve  F  annual 
output  in  kilowatt-hours.  Curve  G  number  of  customers. 

the  plant  have  increased  to  $96,881.00*  (on  July  31,  1910)  al- 
though the  bond  interest  of  $1,925  per  year  is  paid  out  of  the 
earnings  of  the  plant.  In  judging  the  financial  success  of  the 

*  $133,000  assets  minus  $36,119  of  accumulated  depreciation  as  carried  forward 
on  the  books. 


ELECTRIC   LIGHTING. 


plant,  however,  one  must  remember  that  it  pays  no  taxes.  The 
ordinates  of  curve  A,  Fig.  13,  show  the  growth  of  assets  year 
by  year.  In  reckoning  these  assets  the  plant  equipment*  is 
estimated  at  its  first  cost,  and  the  assets  include  an  increasing 
stock  of  electric  lighting  supplies  (new),  and  interest-bearing 
loans  and  bonds.  The  latter  amounted  to  $13,243.50  on  August 


35 


'5 


10 


H 


JL 


A 


1901          1903          1905        1907         1909          1911 

Fig.  15.     Curve   H   yearly  operating  expenses.     Curve   I   yearly  income. 

I,  1910.  The  ordinates  of  curve  B  represent  the  accumulated 
depreciation  charge  of  5  per  cent,  per  year  which  a  municipal 
plant  in  Connecticut  is  required  by  law  to  carry  forward  in  its 
annual  reports. 

*  Permanent  equipment,  only,  is  included.     Lamps  and  other  materials  which 
are  discarded  after  short  periods  of  use  are  not  included. 


COSTS   AND   SELLING   PRICE.  31 

The  ordinates  of  the  curves  in  Fig.  14  show  the  year  by  year 
growth  of  the  following  items: 

Curve  C  shows  the  plant  capacity  expressed  in  5O-watt  units 
(lamps) . 

Curve  D  shows  the  connected  lighting  load  expressed  in 
5O-watt  units  (lamps). 

Curve  E  shows  the  connected  load  of  motors  and  heating 
apparatus  expressed  in  5O-watt  units. 

Curve    F  shows  the  yearly  kilowatt-hours  output. 

Curve   G   shows  the  number  of  customers. 

Fig.  15  shows  the  year  by  year  growth  of  the  following  items: 

Curve  H  shows  yearly  operating  expenses  including  the  cost 
of  maintaining  the  fire-alarm  system. 

Curve  /  shows  yearly  income  including  $500.00  per  year  paid 
by  the  Borough  for  the  maintenance  of  the  fire-alarm  system. 

INVESTMENT  (1907). 

Station  building  and  real  estate $12,346.38 

Steam  equipment 21,435.65 

Electric  equipment 13,437.04 

Line  equipment,  including  street  lighting  circuits 25,068.29 

Transformers 3.523.72 

Incandescent  lamps 3,520.16 

Meters 473-73 

Arc  lamps  and  arc  lamp  supplies 1,008.72 

Average  amount  of  coal  and  supplies  on  hand 2,500.00 

Total  capital  invested $83,313.69 

OPERATING   EXPENSES  (1907). 

Maintenance  of  lamps* $1,200.51 

Trimming  and  maintaining  arc  lamps 682.82 

Labor  and  superintending 4,896.93 

Coal  (at  $4.00  per  ton) 7,409.72 

Oil  and  waste 147-97 

Building  and  boiler  insurance 374-13 

Liability  insurance 288.00 

Office  rent 30.00 

Plant  stationery  and  incidentals 1,622.13 

Total  expenses $16,652.21 

*  Customers  are  supplied  with  new  lamps  as  the  old  ones  burn  out. 


ELECTRIC    LIGHTING. 


Kilowatt-hours  output  during  the  year 464,000 


3^2  per  cent,  interest  on  in- 
vestment   .$2,916.00 

4  per  cent,  depreciation  on 

equipment 2,740.00 

Total  cost  per  kilowatt- 
hour  0.048 


6  per  cent,  interest  on  in- 
vestment  $4,999.00 

4  per  cent,  depreciation  on 

equipment 2,740.00 

i  per  cent,  taxes  on  $80,000      800.00 

Total  cost  per  kilowatt- 
hour  0.0543 


INCOME  (1907). 

For  street  lighting $  6,513.36 

For  commercial  lighting 21,422.47 

For  maintenance  of  fire-alarm  system 500.00 


Profits  in  excess  of  3)^  Per 
cent,  interest  and  4  per 
cent,  depreciation $6,118.00 


Profits  in  excess  of  6  per  cent, 
interest  and  4  per  cent,  de- 
preciation and  i  per  cent, 
taxes $3,245.00 


The  foregoing  tables  show  the  details  for  the  year  ending 
July  31,  1907.  In  order  to  show  the  important  relations  between 
investment,  operating  expenses,  and  income,  the  newly  pur- 
chased water-power  plant  (which  was  not  operated  during  1907) 
is  not  included  as  a  part  of  the  investment. 

It  may  seem  that  the  profits  should  be  much  greater  than 
what  is  indicated  in  the  table  in  view  of  the  fact  that  the  actual 
cost  per  kilowatt-hour  is  about  5  cents  whereas  the  lighting  rate 
is  II  cents  per  kilowatt-hour;  but  the  sum  of  all  customers' 
meter  readings  is  less  than  the  station  output  because  of  dis- 
tribution losses,  and  off-peak  service  is  sold  at  much  less  than  1 1 
cents  per  kilowatt-hour. 

The  cost  of  maintaining  the  fire-alarm  system  cannot  be  clearly 
separated  from  other  items  of  expense.  In  fact  the  charge  of 
$500  is  about  equal  to  the  cost,  which  includes  care  of  fire-alarm 
apparatus  and  lines,  and  fuel  and  labor  for  keeping  up  steam  for 
the  whistle  during  the  daytime. 

The  schedule  of  service  rates  in  force  in  1907  was  a  complicated 
mixture  of  flat  rates  and  meter  rates,  and  a  knowledge  of  this 
schedule  beyond  the  mere  fact  that  it  represented  approximately 
a  meter  rate  of  1 1  cents  per  kilowatt-hour  is  not  necessary  to  an 
understanding  of  the  economies  of  the  plant  during  1907. 


COSTS   AND    SELLING   PRICE. 


33 


MISCELLANEOUS    ITEMS  (1907). 

Total  station  capacity  expressed  in  5o-watt  units  (lamps)  .....  9,000 

Total  connected  load  (commercial)  in  5o-watt  units  ...........  13,316 

Street-lighting  load  expressed  in  5o-watt  units  (lamps)  ........  1,000 

3  street-lighting  circuits,  aggregate  length  of  in  miles  .........  26.5 

Length  of  street  covered  by  2-wire  high-voltage  line  (primary 

circuits)  in  miles  ......................................  14.4 

Length  of  street  covered  by  3-wire  low-voltage  line  (secondary 

circuits)  in  miles  .......................................  6.8 

Number  of  transformers  in  service  ..........................  58 

Aggregate  capacity  of  transformers  in  kilowatts  ..............  346 

Rate  charged  per  year  for  enclosed-arc  street  lamps  in  dollars.  .  69.58 

Commercial  lighting  rate  per  kilowatt-hour  in  cents  ..........  n 

Plant  in  operation  about  14  hours  per  day  on  the  average. 


V 


Aug. 


Oct. 


Dec.        Feb. 

Fig.  16. 


Apr.        June 


The  ordinates  of  the  curves  in   Fig.    16  show  the  average 
monthly  bills  of  the  customers  of  the  Wallingford  station  after 
meters  were  installed  and  the  service  changed  to  a  meter  basis. 
4 


34 


ELECTRIC    LIGHTING. 


Curve  A  refers  to  a  group  of  customers  having  an  average  of  50 
connected  lamps,  curve  B  refers  to  a  group  of  customers  having 
an  average  of  30  connected  lamps,  and  curve  C  refers  to  a  group 
of  customers  having  an  average  of  20  connected  lamps.  Indi- 
vidual monthly  bills  depart  very  widely  from  the  averages  shown 


in  Fig.  1 6,  and  the  ordinates  of  the  curves  a,  b  and  c  in  Fig.  17 
show  the  probable  departure*  of  an  individual  bill  from  the  mean. 
For  example,  the  ordinate  of  curve  a  for  December  is  $2.21, 
which  means  that  the  December  bill  of  any  customer  taken  at 
random  is  as  likely  to  depart  ess  than  $2.21  from  the  mean  as  it 
is  to  depart  more  than  $2.21  from  the  mean  for  December  ($7.18, 
see  Fig.  16). 

*  Reckoned  exactly  as  the  "probable  <yrror  of  a  single  observation"  is  reckoned 
in  the  theory  of  least  squares. 


COSTS   AND    SELLING   PRICE.  35 

The  bills  of  the  lo-lamp  customers  are  not  shown  in  Figs.  16 
and  17  because  these  ^.bills  come  down  very  frequently  to  the 
fixed  minimum  of  $1.00  per  month.  In  fact  the  mean  of  the 
ro-lamp  customers  is  about  $1.10  per  month  in  midsummer  and 
about  $1.96  per  month  in  midwinter,  and  the  "probable  depar- 
ture" of  an  individual's  bill  from  the  mean  is  about  5  cents  in 
midsummer  and  about  18  cents  in  midwinter. 


CHAPTER   II. 

ELECTRIC  DISTRIBUTION  AND  WIRING. 

16.  Parallel  and  series  systems  of  distribution.* — In  prac- 
tice a  large  number  of  receiving  units  (lamps  or  motors)  are  al- 
ways operated  from  a  single  generator,  and  it  is  always  desirable 
to  put  any  lamp  or  motor  into  service  or  to  take  any  lamp  or 
motor  out  of  service  at  will  without  affecting  the  other  lamps  or 
motors.  The  easiest  method  for  doing  this  is  to  connect  the 
lamps  and  motors  in  parallel  with  each  other  between  supply 
mains  and  maintain  a  constant  voltage  between  the  mains.  In 
this  case  the  receiving  units  must  all  be  of  the  same  voltage  rating, 
and  a  given  unit  is  taken  out  of  service  by  opening  its  circuit. 
This  arrangement  constitutes  what  is  called  the  constant-voltage 
system  of  distribution  and  it  is  frequently  called  the  parallel 
system  of  distribution.  Another  method  is  to  connect  the  lamps 
or  motors  in  series  and  to  maintain  a  constant  current  through 
the  circuit.  In  this  case  the  receiving  units  must  all  be  of  the 
same  current  rating,  and  a  given  unit  is  taken  out  of  service  by 
short-circuiting  it  by  means  of  a  by-pass  switch.  This  arrange- 
ment constitutes  what  is  called  the  constant-current  system  of 
distribution  and  it  is  frequently  called  the  series  system  of  dis- 
tribution. 

The  constant-voltage  system  is  almost  universally  used  now- 
adays both  for  direct  current  distribution  and  for  alternating 
current  distribution.  This  system  is  exemplified  by  great  num- 
bers of  plants  for  supplying  current  to  lamps  and  motors  in  our 
cities,  by  nearly  every  electric  railway  installation,  and  by 
numerous  installations  for  the  long  distance  transmission  of 
power. 

*  A  brief  discussion  of  these  two  systems  (with  special  reference  to  the  char- 
acteristics of  the  generators)  is  given  in  Dynamos  and  Motors,  The  MacmiUan  Co, 

36 


ELECTRIC    DISTRIBUTION   AND  WIRING.  37 

The  constant-current  system  of  supply  is  advantageous  when  a 
fixed  number  of  widely-distributed  lamps,  arc  or  incandescent, 
are  to  be  operated ;  the  lamps  are  connected  in  series  and  supplied 
with  constant  current.  This  system  is  exemplified  by  many 
street-lighting  installations  and  by  the  Thury  system*  of  power 
transmission. 

Combinations  of  series  and  parallel  connections,  (a)  Connections 
of  series-groups  in  parallel. — When  the  voltage  of  supply  in  the 
constant-voltage  method  of  distribution  is  greater  than  can  be 
conveniently  used  for  operating  single  lamps,  the  lamps  are 
usually  arranged  in  groups,  each  group  consisting  of  a  number  of 
lamps  connected  in  series,  and  these  groups  of  lamps  are  con- 
nected in  parallel  with  each  other  across  the  mains.  This  ar- 
rangement is  exemplified  in  the  lighting  of  electric  cars  where  the 
standard  supply  voltage  is  550  volts  and  where  the  lamps  for 
lighting  the  cars  are  usually  no-volt  lamps  connected  in  series- 
groups  of  5  lamps  each,  these  groups  being  connected  in  parallel 
with  each  other  between  the  trolley  and  the  rail.  A  similar 
arrangement  is  frequently  employed  for  tungsten  lamps,  es- 
pecially in  the  case  of  the  low-candle-power  tungsten  lamps 
which  are  extensively  used  for  decorative  and  sign  lighting. 
Thus  five  22 -volt  tungsten  lamps  may  be  connected  in  a  series- 
group,  and  such  groups  may  be  connected  in  parallel  with  each 
other  across  standard  no-volt  mains. 

(b)  Connections  of  parallel-groups  of  lamps  in  series. — In  the 
early  days  of  electric  lighting  the  constant-current  method  of 
supplying  arc  lamps  for  street  lighting  was  quite  common.  Many 
towns  which  were  provided  with  this  series  system  of  distribution 
were  not  provided  with  any  other  means  for  supplying  incandes- 
cent lamps,  and  the  only  feasible  method  for  operating  incan- 

*  The  Thury  system  (direct-current)  is  a  constant-current  system  of  distribution. 
It  is  exemplified  by  several  large,  long-distance,  power-transmission  plants  in 
Europe.  A  description  of  the  Thury  system  is  given  by  Wieshofer  in  the  Zeit- 
schrift  fur  Electrotechnik  (Vienna),  Vol.  XVI,  pages  5-10,  1898.  See  also  a  paper 
by  Cuenod  and  Thury  in  the  Bulletin  de  la  Societete  Internationale  des  Electriciens, 
Vol.  XVII,  pages  9-93,  January,  1900. 


38  ELECTRIC   LIGHTING. 

descent  lamps  was  to  connect  a  group  of  such  lamps  in  parallel 
and  to  connect  this  group  in  series  in  the  arc  lamp  circuit.  This 
arrangement  is  now  seldom  or  never  used. 

Advantages  and  disadvantages  of  the  connections  of  series- groups 
of  lamps  in  parallel. — In  order  to  understand  the  advantages  of 
grouping  electric  lamps  in  series  one  must  keep  in  mind  the  fact 
that  the  electric  lamp  is  essentially  a  low-voltage  device,  so  that 
if  one  wishes  to  use  a  high-voltage  distributing  line  in  order  to 
reduce*  the  amount  of  line  copper  required,  the  lamps  must  be 
arranged  in  series  groups  in  order  to  adapt  them  to  the  high- 
voltage  supply.  The  disadvantage  of  the  series  grouping  of 
lamps  is  that  each  group  must  be  turned  off  and  on  as  a  unit 
unless  a  special  device  is  used  to  connect  an  equivalent  resistance 
in  place  of  a  lamp  which  is  to  be  turned  off. 

The  grouping  of  incandescent  lamps  in  series  is  exemplified 
in  the  use  of  incandescent  lamps  for  street  lighting  When  such 
a  group  is  supplied  with  constant  current  (i.  e.,  with  a  current 
which  is  automatically  kept  at  a  constant  value  regardless  of 
the  number  of  lamps)  then  any  given  lamp  is  simply  short- 
circuited  by  a  by-pass  connection  when  for  any  reason  the  lamp 
is  taken  out  of  service.  When,  however,  such  a  group  is  con- 
nected to  a  constant  voltage  supply  then  when  a  lamp  is  broken 
or  otherwise  damaged  a  by-pass  containing  a  similar  auxiliary 


Fig.  18. 

lamp  must  be  provided.  Thus  Fig.  18  shows  twenty  no-volt 
lamps  connected  in  series  and  supplied  from  2,2OO-volt  mains  in 
a  central  station,  and  Fig.  19  shows  how  each  lamp  in  Fig.  18 
is  provided  with  a  by-pass.  Each  lamp  L  of  the  series  has 
a  similar  auxiliary  lamp  A  connected  in  parallel  with  it,  and 
the  circuit  of  this  auxiliary  lamp  is  broken  by  a  thin  piece  of 

*  See  Art.  23. 


ELECTRIC    DISTRIBUTION   AND    WIRING. 


39 


paper  p  between  two  metal  springs  SS.  If  the  lamp  L  hap- 
pens to  break  the  full  voltage  of  supply  (2,200  volts)  is  brought 
to  bear  upon  the  thin  paper  p,  thus  puncturing  it  and  estab- 
lishing a  metal  bridge  from  spring  to  spring.  In  this  way  the 
auxiliary  lamp  A  is  substituted 
for  the  lamp  L.  The  inspector 
on  his  rounds  seeing  A  burn- 
ing knows  that  a  new  lamp  is 
needed  in  place  of  L,  and  when 
a  new  lamp  is  installed  a  fresh 
bit  of  paper  is  placed  between 
the  springs  SS.  When  a  con- 
stant current  is  supplied  to  a  series  group  of  lamps,  as  shown 
in  Fig.  18,  then  each  lamp  has  a  by-pass  as  shown  in  Fig.  19 
except  that  the  auxiliary  lamp  A  is  not  used. 

17.  The  Edison  three-wire  system  of  distribution. — Figure 

20  shows  a    number   of    no-volt   lamps    connected  in    series- 
groups  of  two  lamps  each  to  22O-volt  mains  and  supplied  with 
current  from  two  I  lo-volt  generators  connected  in  series;  and  Fig. 

21  shows  an  arrangement  which  is  the  same  as  Fig.  20  except 


Fig.  19. 


O  C 


O  C 


O  0  O  C 


>  C 


Q  0  0  6  O  O 


000000006 


Fig.  20. 

that  a  third  main  CD  is  added  as  shown.  By  placing  some  of 
the  lamps  of  each  customer  in  the  A  -set  and  some  in  the  B-set 
(see  Fig.  21),  there  will  always  be  nearly  the  same  number  of 
lamps  in  each  set  even  when  each  customer  exercises  entire 


ELECTRIC   LIGHTING. 


freedom  in  the  turning  off  and  on  of  single  lamps;  under  these 
conditions  the  middle  main  need  never  carry  very  much  current, 
and  therefore  the  middle  main  may  be  made  of  comparatively 
small  wire.  In  fact  the  current  in  the  middle  main  will  be  a 
small  current  coming  into  the  station  when  the  A  -set  contains 
a  few  more  lamps  than  the  J3-set,  or  a  small  current  going  out 


O  Q  OC 


0  C 


OO  O  C 


)  O  O  O  O  O  O  C 


B-set 


Fig.  21. 

from  the  station  when  the  5-set  contains  a  few  more  lamps 
than  the  A  -set.  In  this  arrangement,  therefore,  most  of  the 
advantage  (economy  of  line  copper)  due  to  the  use  of  220-volt 
distribution  is  realized  although  no-volt  lamps  are  used.  The 
arrangement  is  called  the  Edison  three-wire  system  of  distribution. 
In  practice  the  middle  main  is  usually  made  of  the  same  size 
of  wire  as  each  outside  main  but  each  outside  main  need  be 
only  one-quarter  as  heavy*  as  would  be  required  to  supply  the 
same  number  of  lamps  in  the  simple  parallel  system  using  no 
volts.  Therefore  to  supply  a  given  number  of  no-volt  lamps 
in  the  Edison  three-wire  system  requires  only  three  eighths  as 
much  copper  in  the  mains  as  would  be  required  in  the  simple 
parallel  system  of  distribution  with  the  same  percentage  drop 
of  voltage. 

When  the  number  of  lamps  in  the  A  -set  in  Fig.  21  is  different 
from  the  number  of  lamps  in  the  .B-set  the  system  is  said  to  be 
unbalanced.  When  the  system  is  unbalanced  the  middle  main 

*  See  Art.  23,  page  57. 


ELECTRIC   DISTRIBUTION   AND   WIRING.  41 

carries  current  as  above  explained,  and  the  voltage  drop  in  the 
middle  main  tends  to  increase  the  voltage  which  acts  on  one 
set  of  lamps  and  to  decrease  the  voltage  which  acts  on  the  other 
set  of  lamps.  These  voltage  relations  are  clearly  represented 

100  amperes 


L 


^  to  amperes 


5 

^  90  amperes 

>J 

Fig.  22a. 


for  a  particular  case  in  Figs.  220,  and  22b.  These  figures  show 
the  state  of  affairs  when  the  A  -set  of  lamps  takes  100  amperes 
and  the  £-set  takes  90  amperes,  each  main  having  1/20  ohm 


too  amperes 


90  amperes 
Fig.  22&. 


resistance;  the  lamps  being  supposed  to  be  bunched  at  the  ends 
of  the  mains  for  the  sake  of  simplicity.  Electric  current  may 
always  be  considered  as  flowing  downhill,  as  it  were,  so  that 
the  electric  level  (or  potential)  is  to  be  thought  of  as  falling  off 


42  ELECTRIC   LIGHTING. 

along  each  main  in  the  direction  of  the  current  as  indicated 
by  the  fine  inclined  lines  in  Fig.  22b.  The  distances  between 
the  inclined  lines  at  the  ends  of  the  mains  represent  the  volt- 
ages acting  on  the  two  sets  of  lamps.  Thus  the  voltage  b  acting 
on  the  A  -set  is  115  volts  —  5  volts  —  %  volt  =  109.5  vo'ts,  and 
the  voltage  d  acting  on  the  J5-set  is  115  volts  —  4.3/2  volts  +  J/2 
volt  =in  volts. 

1 8.  Special  three-wire  generators  and  three- wire  balancers 
for  direct-current  systems. — The  use  of  two  generators  as 
indicated  in  Figs.  21  and  22  involves  an  added  expense  for 
machinery  in  a  generating  station  and  the  extensive  use  of 
the  Edison  three-wire  system  has  given  rise  to  the  so-called 
three-wire  generator  which  can  be  used  for  supplying  current 
to  a  three-wire  system,  and  to  the  so-called  three-wire  balancer 
which  enables  a  single  22O-volt  generator  of  the  ordinary  type 
to  supply  a  no- volt  Edison  three-wire  system. 

The  double-current  generator. — Several  types  of  three-wire 
generators  have  been  proposed  and  used  to  some  extent*  but 
the  machine  which  is  now  almost  universally  used  to  deliver 
direct  current  to  the  Edison  three-wire  system  is  the  synchronous 
converter  (rotary  converter).  This  machine  when  engine 
driven  is  called  the  double-current  generator '.f  The  arrange- 
ment of  the  three-ring  double-current  generator  as  a  three- 
wire  direct-current  generator  is  shown  in  Fig.  23.  Three  sim- 
ilar choke  coils  (inductance  coils)  C ',  C"  and  C'"  are  connected 
as  shown  to  the  middle  main  and  the  other  ends  a,  b  and  c  of 
the  coils  are  connected  to  the  alternating-current  brushes, 
a,  b  and  c,  of  the  machine 

The  motor-generator  balancer. — The  two  generators  shown  in 
Fig.  21  may  be  replaced  by  a  single  22O-volt  generator  of  the 
ordinary  type  (having  two  brushes),  and  the  current  which 

*  The  three-wire  generator  of  Dettmar  is  described  in  Electrotechnische  Zeit- 
schrift,  Vol.  XVIII,  pages  55  and  320,  1897. 

t  The  structural  features  of  the  double-current  generator  (rotary  converter) 
are  described  in  Art.  145  of  Dynamos  and  Motors. 


ELECTRIC    DISTRIBUTION   AND   WIRING. 


43 


flows  into  or  out  of  the  station  on  the  middle  main  may  be 
taken  care  of  by  a  small  motor-generator  consisting  of  two 
simple  shunt-wound  clynamos  P  and  Q  with  their  armatures 

outside  main 


110' volts 


110  volts 


/d.c.  brush   outside  main \___ 

Fig.  23.     Terminals   a,  b  and   c  connected  to  brushes    a,  b   and   c   respectively. 

mounted  on  one  shaft  and  connected  electrically  as  shown  in 
Fig.  24.  Consider  the  particular  case  in  which  the  upper  main 
carries  a  large  outward  current  of  100  amperes,  the  middle 
main  a  return  current  of  10  amperes,  and  the  lower  main  a  return 
current  of  90  amperes  as  shown  in  the  figure.  Assuming  the 
efficiency  of  the  motor-generator  to  be  100  per  cent,  (for  the 


100  amperes 


10  amperes 


go  amperes 


Fig.  24. 


sake  of  simplicity  of  statement),  the  action  would  then  be  as 
follows:  One-half  of  the  current  entering  the  station  on  the 
middle  main  would  flow  downhill,  as  it  were,  through  P  to  the 
negative  terminal  of  the  large  generator;  P  would  therefore  act 


44 


ELECTRIC    LIGHTING. 


as  a  motor,  drive  Q  as  a  generator,  and  cause  Q  to  pump  the 
remainder  of  the  current  in  the  middle  main  uphill,  as  it  were, 
to  the  positive  terminal  of  the  large  generator.  With  outward 
current  flowing  in  the  middle  main  Q  would  operate  as  a  motor 
and  P  would  operate  as  a  generator.  In  order  to  keep  the  poten- 
tial of  the  middle  main  at  the  proper  value  so  as  to  divide  the 
electromotive  force  of  the  large  generator  into  two  equal  parts, 
the  machines  P  and  Q  must  have  carefully  adjusted  compound 
field  windings,  or  the  field  rheostat  of  P  or  Q  must  be  repeatedly 
adjusted  as  the  current  in  the  middle  main  changes  in  value. 

In  the  use  of  a  motor-generator  balancer  it  is  desirable  to  keep 
the  system  approximately  balanced  so  as  to  reduce  the  duty  of 
the  motor-generator.  By  carefully  grouping  the  consumers' 
lamps  and  motors,  the  unbalancing  of  a  3-wire  system  may  be 
usually  kept  within  8  or  10  per  cent,  and  under  these  conditions 
the  rated  output  capacity  of  each  of  the  dynamos  P  and  Q  in 
Fig.  24  would  need  to  be  only  8  or  10  per  cent,  of  the  rated 
output  capacity  of  the  main  generator. 

19.  The  supply  of  alternating  current  to  an  Edison  three-wire 
system. — A    transformer    with    a    divided    secondary    coil    can 
street  main 


street  main 


primary  coil 

m^moo 

secondary  coils 


110  volts 


to  lamps 


110  volts      to  lamps 


Fig.  25. 

be  used  to  supply  alternating  current  to  an  Edison  three-wire 
system  by  arranging  connections  as  shown  in  Fig.  25;  or  two 
independent  transformers  can  be  used  for  the  same  purpose  as 
shown  in  Fig.  26. 


ELECTRIC    DISTRIBUTION   AND   WIRING. 


45 


The  Edison  three-wire  system  must  not  be  confused  with  the 
polyphase  three-wire  system.*  The  fundamental  idea  in  the 
Edison  three-wire  system  is  to  deliver  current  to  two  approxi- 
mately similar  groups  of  lamps  in  series,  as  explained  in  Art.  17; 
and  the  fundamental  idea  of  the  polyphase  system  is  to  deliver 
alternating  currents  from  electrically  separate  alternators  over 
separate  lines  to  separate  receivers. 

street  main 


street  main 

1100  vol\ 
| 

A 

primary 

OfYYV^on  ] 
k^Vxjyyyvy/ 

[-transformer          1 

primary 
^-transformer 

secondary  secondary  ' 

110  volts     to  lamps 


110  volts    to  lamps 


Fig.  26 

20.  Factors  which  determine  the  size  of  wires  in  practice. 

—There  are  five  conditions  which  should  be  considered  in  select- 
ing the  sizes  of  wires  for  the  distribution  of  electric  current, 
namely,  (a)  the  wire  must  have  sufficient  strength  to  withstand 
the  mechanical  stresses  to  which  it  may  be  subjected.  This 
condition  applies  especially  to  wires  strung  on  poles,  (b)  The 
wire  must  be  large  enough  to  carry  the  prescribed  current  without 
becoming  so  hot  as  to  damage  its  insulation  or  ignite  adjacent 
inflammable  material.  This  condition  applies  especially  to  wires 
in  a  building,  (c)  The  wire  must  be  large  enough  to  keep  the 
variations  of  voltage  at  the  lamps  or  other  receiving  units  within 
certain  limits.  This  condition  applies  only  to  the  distributing 
wires  of  a  "constant-voltage"  system.  See  Art.  23.  (d)  The 
wire  should  be  large  enough  so  that  the  annual  value  of  the  RI2 
losses  in  the  wire  are  not  greater  than  the  interest  on  the  cost 


*  See  Arts,  117-120  of  Dynamos  and  Motors, 


46  ELECTRIC    LIGHTING. 

of  the  wire.  See  Art.  26.  (e)  In  extreme  cases  the  size  of  a 
wire  may  be  determined  by  a  consideration  of  the  electric  strength 
of  the  air  or  other  insulating  substance  surrounding  the  wire 
because  the  ability  of  an  insulating  medium  to  withstand  the 
electric  stress  between  two  wires  due  to  a  given  voltage  between 
the  wires  depends  in  part  upon  the  size  and  shape  of  the  wires. 
See  Art.  27. 

Whenever  in  a  given  case  any  one  of  these  conditions  demands 
a  larger  wire  than  would  be  required  by  any  of  the  other  condi- 
tions, the  larger  wire  should  be  used.  Frequently  an  engineer 
is  guided  by  one  only  of  the  above  conditions  in  laying  out  the 
preliminary  plans  for  a  distributing  system.  When  this  is  the 
case  the  preliminary  plans  should  be  examined  carefully  to  see 
that  all  of  the  conditions  are  satisfied  before  the  plans  are  finally 
adopted. 

21.  Mechanical  stresses  in  aerial  wires  and  their  supports.* 
Stresses  in  the  supports. — The  stresses  in  the  insulator  pins, 
cross-arms,  and  poles  are:  (a)  The  stresses  due  to  the  weight  of 
the  wire  plus  the  weight  of  an  occasional  coating  of  ice;  this 
weight  is  to  be  considered  as  resting  directly  upon  the  insulators 
and  constituting  a  force  acting  vertically  downwards. f  (b)  The 
stresses  due  to  the  unbalanced  tensions!  of  the  wire  on  the 
opposite  sides  of  an  insulator.  The  tensions  of  the  wire  on  the 
opposite  sides  of  an  insulator  are  in  nearly  every  case  sensibly 
equal  in  value  and  unbalancing  occurs  only  where  the  wire  termi- 
nates or  changes  its  direction.  In  the  case  of  a  straight  pole-line 
on  a  slope  the  tension  of  the  wire  is  generally  greater  on  the 
down-hill  side  of  the  pole,  but  the  unbalanced  force  is  in  this  case 
a  force  acting  vertically  downwards,  that  is,  a  given  insulator 

*  A  discussion  of  the  details  of  pole-line  construction  is  beyond  the  scope  of  this 
text.  Information  concerning  these  details  may  be  found  in  Electrical  Transmission 
of  Energy,  A.  V.  Abbott,  1905  edition,  Chapter  III. 

t  This  force  is  the  sum  of  the  vertical  components  of  the  tension  of  the  wire  on  the 
two  sides  of  an  insulator. 

J  Horizontal  components  of  the  tensions,  inasmuch  as  vertical  components  are 
considered  under  (a). 


ELECTRIC    DISTRIBUTION   AND   WIRING. 


47 


supports  a  large  part  of  the  weight  of  the  lower  span  of  wire  and 
a  correspondingly  small  part  of  the  weight  of  the  upper  span  of 
wire,  (c)  Stresses  due  to  wind  pressure. 

(i)  The  weight  of  wire  and  ice  produces,  in  the  poles  and  pins,  stresses  of  simple 
compression,  which  stresses  may  nearly  always  be  neglected,  inasmuch  as  poles  and 
pins  which  are  strong  enough  to  withstand  the  bending  stresses  to  which  they  are 
subjected  are  not  perceptibly  affected  by  these  slight  stresses  of  compression. 

The  weight  of  wire  and  ice  produces  a  bending  stress  in  the  cross-arms,  and  the 
breadth,  b,  and  depth,  d,  of  the  cross-arms  must  be  sufficient  to  sustain  this  bending 
stress,  the  length  of  the  cross-arms  being  determined  by  the  number  of  wires  and 
their  required  distance  apart.  The  simplest  case  is  that  shown  in  Fig.  27,  which 


Fig.  27. 

shows  a  cross-arm  carrying  two  wires.     In  this  case  the  dimensions,  b,  d,  and  /,  as 
shown  in  the  figure  must  satisfy  the  equation: 

6WI 


C    .....   __„ 


(i) 


in  which  S  is  the  permissible  fiber  stress  of  the  cross-arm  material  in  pounds  per 
square  inch  at  the  points,  TT,  Fig.  27,  and  W  is  the  total  weight  in  pounds  resting 
on  one  pin.  The  dimensions,  b,  d,  and  /,  are  expressed  in  inches. 

A  coating  of  ice  one  eighth  of  an  inch  thick  is  seldom  exceeded,  and  it  is  cheaper 
to  repair  the  line  after  an  excessively  severe  sleet  storm  than  it  is  to  make  it  strong 
enough  to  sustain  much  more  than  one  eighth  of  an  inch  of  ice  on  the  wires. 

The  permissible  values  of  5  may  be  taken  from  the  table  of  tensile  strengths  of 
timber. 


48  ELECTRIC    LIGHTING. 

(2)  The  stresses  due  to  unbalanced  tensions  are  the  most  important  stresses  to  be 
considered  in  pins  and  poles.  Having  given  the  value  of  the  tension  and  the  angle 
turned  at  a  corner,  the  side  force,  W,  Fig.  27,  is  easily  determined,  and  the  dimen- 
sions, I'  and  d'  (diameter  of  pin  at  base),  Fig.  27,  must  satisfy  the  equation: 


in  which  S'  is  the  maximum  permissible  fiber  stress  in  pounds  per  square  inch,  W  is 
the  resultant  horizontal  force  in  pounds  acting  on  the  insulator,  and  /'  and  dr  are  ex- 
pressed in  inches. 

The  cross-arms  on  a  corner  pole  are  usually  set  so  as  to  be  parallel  to  the  resultant 
force  due  to  wire  tensions,  and  hence,  except  at  the  end  of  a  line,  this  resultant  force 
does  not  produce  a  bending  stress  in  the  cross-arms. 

The  unbalanced  tensions  of  the  wires  produce  bending  stresses  in  the  poles;  and 
the  diameter,  dr,  of  the  pole  at  the  ground  and  the  height,  /',  of  the  pole,  both  in 
inches,  must  satisfy  equation  (2),  using  for  W  the  resultant  horizontal  force  due  to 
all  of  the  wires.  In  most  cases  a  corner  pole  is  guyed  or  braced  so  that  the  bending 
stress  in  the  pole  is  to  a  great  extent  eliminated. 

(3)  Stresses  due  to  wind  pressure  vary  with  the  direction  as  well  as  the  velocity 
of  the  wind.  When  the  wind  blows  parallel  to  the  line  its  effect  is  slight  because  the 
wires  are  parallel  to  the  wind.  It  is  considered  sufficient  in  practice  to  provide  the 
necessary  strength  to  withstand  a  side  wind  giving  a  maximum  pressure  of  from  20 
to  30  pounds  per  square  foot  of  surface,  according  to  the  degree  of  exposure  of  the 
line.  In  calculating  the  force  of  a  side  wind  on  a  cylinder  like  a  pole  or  wire,  the 
effective  exposed  area  is  taken  as  two  thirds  of  the  product  of  the  diameter  of  the 
cylinder  times  its  length. 

The  effect  of  a  side  wind  is  to  produce  bending  stresses  in  the  insulator  pins  and 
in  the  poles,  and  the  dimensions  of  the  pin  in  inches,  as  shown  in  Fig.  27,  must 
satisfy  equation  (2),  where  W  is  the  total  force  of  the  wind  on  the  wire  in  pounds, 
and  S'  is  the  maximum  permissible  fiber  stress  in  pounds  per  square  inch.  Also 
the  height  of  V  of  the  pole  and  its  diameter,  df,  at  the  ground,  both  in  inchest 
must  satisfy  equation  (2),  in  which  case  W  is  the  force  of  the  wind  on  all  the 
wires  plus  about  half  or  two  thirds  of  the  force  of  the  wind  upon  the  pole  and  cross- 
arms. 

In  estimating  the  stresses  on  pin,  cross-arm  and  pole,  due  to  weight  of  wire 
and  ice,  or  the  stresses  due  to  wind  pressure  on  the  wires,  a  length  of  wire  equal 
to  the  distance  between  adjacent  poles  must  be  assumed  to  be  supported  by  each 
insulator. 

TENSILE    STRENGTH  OF    TIMBER  IN    POUNDS  PER    SQUARE  INCH. 
Cedar  (American)  ..........................................    11,000 

Chestnut  .........................................    7,000  to  13,000 

Cypress  ..................................................     6,000 

Elm  ..............................................   6,000  to  10,000 

Oak  ......................................................    10,000 

Pitch  pine  ................................................      7,600 

Yellow  pine  .......................................   5,000  to  12,060 


ELECTRIC    DISTRIBUTION   AND   WIRING.  49 

White  pine 8,000 

Red  wood  (California) 11,000 

Spruce S.ooo  to  10,000 

The  usual  factor  of  safety  being  4  to  6,  the  permissible  fiber  stress  in  pounds  per 
square  inch  is  from  one  sixth  to  one  fourth  of  the  values  given  in  this  table. 

Stresses  in  the  wire. — In  stringing  a  wire  on  poles  two  things 
in  particular  should  be  provided  for,  namely,  (a)  an  approximate 
equality  of  wire  tension  on  the  two  sides  of  each  insulator,  and 
(b)  a  certain  maximum  tension  in  the  wire  when  it  is  shortened 
by  the  coldest  winter  weather. 

The  first  condition  is  desirable  not  only  because  it  relieves  the 
pins,  cross-arms,  and  poles  from  unnecessary  stress,  but  also 
because  it  is  difficult  to  tie  a  line  wire  to  an  insulator  so  that  it 
cannot  slip  lengthwise  through  the  tie,  unless  the  line  wire  is  bent, 
which  it  should  not  be  if  it  can  be  avoided.  The  horizontal  com- 
ponents of  the  wire  tension  can  always  be  made  equal  on  the 
two  sides  of  an  insulator;  but  in  the  case  of  a  pole  line  on  a 
grade  the  vertical  component  of  the  wire  tension  will  be  somewhat 
greater  on  the  down-hill  side  of  an  insulator  when  the  horizontal 
components  are  equal. 

The  second  condition  is  explained  in  the  following  discussion. 

Pole  line  on  a  level. — The  calculation  of  the  tension  in  a  span  of  wire  in  terms 
of  length  of  span,  vertical  sag  at  the  center  of  the  span,  and  weight  of  the  wire,  or 
the  calculation  of  the  sag  corresponding  to  a  prescribed  tension,  is  based  upon  the 
equation  of  the  curve  formed  by  the  wire.  When  the  sag  is  a  small  fraction  of  the 
length  of  the  span,  say  one  twentieth  or  less,  the  curve  formed  by  the  wire  is  sensibly 
a  parabola  and  the  working  formulae  are: 

*-S  «> 

and 

s-l  +  ^ 

in  which  T  is  the  tension  of  the  wire  in  pounds,  /  is  the  length  of  the  span  in  feet,  h 
is  the  sag  at  the  center  of  the  span  as  shown  in  Fig.  28,  5  is  the  length  in  feet  of  the 
wire  in  a  span,  and  w  is  the  weight  of  the  wire  in  pounds  per  foot.  Equation  (3) 
gives  the  tension  of  the  wire  at  the  center  of  the  span.  The  tension  at  the  ends  of 
the  span  is  wh  pounds  greater  than  at  the  center;  but  this  difference  amounts  to 
only  2  per  cent,  when  the  sag  is  one  twentieth  of  the  length  of  the  span,  and  it  is 
always  negligible.  The  important  use  of  equation  (4)  is  in  making  allowance  for 
the  effects  of  changes  of  temperature, 
5 


50  ELECTRIC   LIGHTING. 


Equation  (3)  when  solved  for   I   gives: 


8hT' 


where  Tf  represents  the  maximum  safe  tension  of  the  wire  in  pounds,  which  is  equal 
to  the  breaking  tension  Tj>  in  pounds  divided  by  the  factor  of  safety.  See  following 
tables. 

The  spacing  of  the  poles  is  usually  chosen  tentatively  as  the  first  step  in  the  design 
of  a  pole  line.  When  a  great  deal  depends  upon  the  permanence  of  a  line,  as  in  a 
transmission  line  supplying  power  to  many  customers,  the  poles  are  placed  close 
together  in  order  to  make  the  line  substantial  and  in  order  that  the  sag  may  be  small 
enough  to  avoid  the  possibility  of  the  wires  swaying  into  contact.  Close  spacing  is 
especially  necessary  in  the  case  of  heavy  wires  so  as  to  distribute  the  weight  of  the 
heavy  wire  over  a  large  number  of  insulators,  the  insulator  being  one  of  the  weakest 
elements  in  the  construction.  Poles  are  usually  spaced  as  follows  on  straight-pole 
lines:  (a)  Heavy  power  transmission  lines  about  80  feet,  which  is  the  spacing  on  the 
Niagara-  Buffalo  transmission  line;  (&)  ordinary  electric-lighting  circuits  in  city  or 
suburban  districts,  from  100  to  125  feet;  (c)  telegraph  and  telephone  lines  125  to 
150  feet.  In  every  case  the  poles  should  be  placed  near  together  where  the  pole  line 
follows  a  curve,  thus  making  the  line  turn  a  very  obtuse  corner  at  each  pole,  in  order 
to  avoid  excessive  stresses  in  the  supporting  structure  due  to  unbalanced  tensions 
of  the  wire.  Furthermore  pole  spacing  is  often  determined  by  surrounding  local 
conditions  such  as  the  presence  of  obstacles  or  the  recurrence  of  cross-streets  in  cities. 

The  amount  of  sag  in  a  span  of  line  wire  should  be  small  in  order  to  prevent  the 
swaying  of  the  wire  by  the  wind.  This  swaying  is  objectionable  because  it  tends  to 
break  the  wire  where  it  is  fastened  to  the  insulators  and  because  it  is  likely  to  bring 
adjacent  wires  into  contact.  Once  the  spacing  of  the  poles  is  chosen,  the  minimum 
permissible  sag  is  determined  as  explained  in  the  next  paragraph;  although  the 
amount  of  sag  that  may  be  allowed  has  a  great  deal  to  do  with  the  choice  of  the  pole 
spacing.  Very  long  spans,  such  as  spans  across  rivers,  have  a  sag  equal  to  one 
twentieth  or  one  thirtieth  of  the  span.  In  ordinary  pole-lines  the  sag  seldom  exceeds 
one  one-hundred-and-fiftieth  of  the  length  of  span,  in  coldest  weather. 

Effects  of  temperature.  —  Wires  are  usually  strung  on  poles  during  warm  weather, 
the  wire  grows  shorter  as  the  temperature  falls,  and  the  tension  of  the  wire  is  there- 
fore greatly  increased  during  cold  winter  weather.  Hence,  it  is  important  to  string  a 
wire  with  sufficient  sag  (and  a  correspondingly  low  tension)  so  that  the  coldest 
weather  may  not  increase  the  tension  of  the  wire  beyond  the  dafe  value,  T'.  Know- 
ing the  temperature,  /,  of  the  wire  when  it  is  strung,  and  the  lowest  winter  temper- 
ature, tf,  the  calculation  of  the  necessary  sag  h,  and  tension,  T,  at  temperature, 
t,  is  carried  out  as  follows:  Take  the  values  of  T'  (=  Tb  divided  by  the  factor  of 
safety)  and  w  from  the  following  tables,  .and  from  these,  together  with  the  chosen 
distance,  I,  between  poles,  calculate  the  winter  sag,  h;,  using  equation  (3),  and 
calculate  the  corresponding  length  of  wire,  s',  in  a  span  using  equation  (4).  Then 
calculate  the  length  of  the  wire  at  summer  temperature,  t,  by  the  equation 

s  =s'(i  +P(t  -  /')] 
in  which  ft  is  the  coefficient  of  linear  expansion  of  the  wire  as  given  in  the  following 


ELECTRIC    DISTRIBUTION   AND   WIRING. 


tables.  From  the  value  of  s,  so  calculated,  the  value  of  the  sag,  h,  at  temper- 
ature, t,  may  be  calculated  from  equation  (4),  and  then  finally  the  tension,  T, 
at  summer  temperature,  t,  may  be  calculated  from  equation  (3). 

It  is  to  be  noted  that  as  a  tine  wire  cools  and  shortens,  its  tension  increases,  so  that 
its  thermal  contraction  is  accompanied  by  an  elastic  elongation  due  to  the  increase 
of  tension;  but  this  effect  is  generally  neglected  in  practical  line  calculations,  inas- 
much as  the  error  is  always  on  the  safe  side,  that  is,  the  actual  winter  tension  is 
less  than  that  anticipated  in  the  calculations. 

It  is  to  be  remembered  that  equations  (3)  and  (4)  are  approximate  because  equa- 
tion (3)  is  based  on  the  assumption  that  the  suspended  wire  forms  a  parabolic 
curve,  and  equation  (4)  is  based  on  the  assumption  that  this  parabola  is  sensibly 
a  circle. 

For  very  long  spans  or  where  the  sag  is  greater  than  about  0.05  of  the  length  of 
span  more  accurate  equations  are  desirable.* 

Pole  line  on  a  grade. — It  is  usual  to  make  the  horizontal  component  of  the  ten- 
sion of  the  wire  the  same  in  value  all  along  a  pole  line  on  a  grade,  so  that  the  actual 
tension  of  the  wire  is  slightly  greater  on  the  down-hill  side  than  on  the  up-hill  side  of 
each  pole.  The  problem  of  determining  the  sag  corresponding  to  a  given  horizontal 
tension,  and  the  problem  of  allowing  for  the  effects  of  temperature  are  treated  in 
the  same  way  as  in  case  of  a  pole  line  on  a  level  except  that  the  following  equations 
are  used  instead  of  equations  (3)  and  (4) : 


T  = 


PHw 


2Hd 


2(H   - 


(5) 


(6) 


in  which  T,  I,  w,  and  5  represent  the  same  quantities  as  in  equations  (3)  and  (4), 
d  is  the  difference  in  level  between  the  ends  of  the  span,  and  H  is  the  sag  of  the  wire 
below  the  upper  end  of  the  span,  as  shown  in  Fig.  29. 

TENSILE  STRENGTHS,  WEIGHTS  AND   COEFFICIENTS  OF 
EXPANSION  OF  WIRES. 


Tensile  Strength 
in  Pounds  per  Circular 
Mil  =  a. 

Density  in  Pounds 
per  Mil-Foot=^. 

/3-Coefficient  of  Linear 
Expansion  per 
Degree  F. 

Steel  

0.0785 

2.65  Xio~6 

O.OOOOO64 

Iron  .  .                 

0.0417 

2.65  Xio~6 

O.OOOOO64 

Hard-drawn  copper  .  . 
Aluminum  

0.0300 
O.O2O4 

3.03  Xio~6 
0.91  Xio~6 

O.OOO0094 
O.OOOOI28 

*  Charts  for  facilitating  these  accurate  calculations  of  long  spans  have  been 
constructed  by  Mr.  Percy  H.  Thomas.  See  Proceedings  American  Institute  of 
Electrical  Engineers,  Vol.  XXX,  pages  1131-1142,  June,  1911. 

Other  important  papers  on  long  spans  are:  W.  LeRoy  Robertson,  Proceedings 
American  Institute  of  Electrical  Engineers,  Vol.  XXX,  pages  1111-1130,  June, 
191 1 ;  Pender  and  Thomson,  Proceedings  American  Institute  of  Electrical  Engineers, 


52  ELECTRIC   LIGHTING. 

Usual  factor  of  safety  from  2  or  3  in  warm  climates  to  6  or  7  in  cold  climates. 

Factor  of  safety  for  aluminum  must  be  larger  than  for  other  metals  on  account  of 
low  elastic  limit  of  aluminum. 

Breaking  tension  of  wire    Tb  =  ad2  in  pounds. 

Weight  of  wire  w  =  bd?  in  pounds  per  foot,  where  d  is  the  diameter  of  the  wire 
in  mils. 

Length  at  t°   F.  =  length  at  *'  X  [i  +  P(t  -  /')]• 

For  weight  of  galvanized  iron  or  steel  wire  add  about  6  per  cent,  to  weight  of 
plain  wire. 

Derivation  of  equations  (j)  to  (6). — Consider  a  wire,  Fig.  28,  suspended  between 
two  points,  p  and  pr.  If  the  wire  is  nowhere  greatly  inclined  the  actual  length 
of  any  element,  ab,  of  the  wire  is  very  nearly  equal  to  the  horizontal  projection, 
dx,  of  the  element.  Therefore  the  weight  of  the  element  is  very  nearly  equal  to 


'///////////////^^^^ 

Fig.  28. 


•w  dx,  w  being  the  weight  of  the  wire  per  unit  length.  Furthermore,  the  horizontal 
component  of  the  tension  of  the  wire  has  necessarily  the  same  value,  T,  all  along 
the  span  of  wire. 

Consider  the  element,  ab,  of  the  wire  of  which  the  coordinates  of  the  end,  a,  are 
x  and  y,  and  the  coordinates  of  the  end,  b,  are  x  +  dx  and  y  +  dy.  Let  dyfdx 
be  the  value  of  the  first  differential  coefficient  of  y  at  the  end,  a,  then  dy/dx 
+<Py /dx-  •  dx  is  its  value  at  the  end,  b.  The  force,  Ta,  pulling  at  the  end,  a,  of 
the  element  is  the  tension  of  the  wire  at  a,  its  horizontal  component  is  T,  and  its 
component  vertically  downwards  is  T  tan  B  or  Tdy/dx.  The  force  Tb  pulling 
at  the  end,  b,  of  the  element  is  the  tension  of  the  wire  at  b,  its  horizontal  component 
is  T,  and  its  component  vertically  upwards  is  T  tan  0'  or  T(dy/dx+d?y/dx*  •  dx). 
Therefore  the  unbalanced  force  pulling  upwards  on  the  element,  ab,  is  Td*y/dx2  -dx, 

Vol.  XXX,  pages  1370-1416,  July,  1911;  and  F.  O.  Blackwell,  Transactions  Inter- 
national Electrical  Congress,  Vol.  II,  pages  331-347,  St.  Louis,  1904. 


ELECTRIC    DISTRIBUTION   AND   WIRING. 


53 


and  this  unbalanced   force  is  equal   to   the  weight  of  the  element,    iv  •  dx,    so 
that- 

*   *  T0  =  w  (i) 

whence 

Ty  =  i^wx*  +  ex  +  c' 

but,  since  y  =  o  and   dy/dx  =  o  when  x  =  o,   the  constants,    c  and  cf,   must  be 
each  equal  to  zero,  so  that: 

w 


From  Fig.  28  it  is  evident  that  y  =  h  when  x  =1/2;  therefore,  substituting 
these  values  in  equation  (ii),  we  have  equation  (3). 

The  second  member  of  equation  (4)  consists  of  the  first  two  terms  of  the  infinite 
series  which  expresses  the  length  of  the  arc  of  a  parabola  in  terms  of  its  chord,  I, 
and  the  distance,  h,  of  the  middle  of  the  arc  from  the  chord. 


W//////////////////^^^ 

Fig.  29. 


Equations  (5)  and  (6)  are  derived  from  equations  (3)  and  (4).  Consider  a 
given  span  of  wire  between  two  poles,  A  and  B,  Fig.  29,  at  a  horizontal  distance, 
/,  from  each  other,  d  being  the  difference  in  level  of  the  tops  of  the  poles,  and  H 
the  sag  of  the  wire  below  the  top  of  pole,  A,  as  shown.  The  given  span,  AB,  may 
be  considered  as  part  of  a  longer  span,  AC,  of  which  the  length  is  L,  as  shown  in 
the  figure;  and  the  portion,  BD,  of  the  given  span  may  be  looked  upon  as  a  span 
also.  Let  5  be  the  length  of  wire  in  the  long  span,  AC,  and  P  the  length  of 
wire  in  the  short  span,  BD.  Then  the  length  of  wire  in  the  given  span,  AB,  is, 


2  2 

Furthermore,  applying  equations  (3)  and  (4)  to  the  span,    AC,    we  have 


m 


(iii) 


(iv) 


and 


54  ELECTRIC   LIGHTING. 

S  =  L  -\ —  (v) 

Applying  equation  (4)  to  the  span,    BD,    gives: 

P  =  (zl  —  L)  -\ — — —  (vi) 

The  equation  of  the  parabolic  curve  formed  by  the  wire  is 

y-*j~f. 

and  at  the  top  of  the  pole,    B,   y  =  H  —  d,   and   x  =  I  —  L/2,   so  that: 


Equations  (5)  and  (6)  are  obtained  by  eliminating  L,  P  and  5  from  (iii)  and 
(iv)  by  means  of  equations  (v),  (vi)  and  (vii). 

22.  Safe  carrying  capacity. — An  electric  wire  rises  in  tem- 
perature until  it  gives  off  heat  to  its  surroundings  as  fast  as  heat 
is  generated  in  it  by  the  current.     Therefore,  the  rise  of  temper- 
ature for  a  given  current  (or  the  current  which  corresponds  to 
a  prescribed  rise  of  temperature)  depends  upon  the  facility  with 
which  the  wire  gives  off  heat  and  this  facility  varies  greatly  with 
the  degree  of  ventilation  in  the  region   in 4  which    the   wire  is 
placed  and  with  the  nature  of  the  adjacent  materials.     Thus  a 
wire  entirely  covered  with  a  wooden  moulding  gets  hotter  than  a 
wire  exposed   to   the  open  air,  and  a  wire  which  lies  against  a 
wooden  wall  gets  hotter  than  a  wire  which  lies  against  a  stone 
wall. 

The  opposite  table  gives  the  safe  carrying  capacity  of  wires 
according  to  the  National  Board  of  Fire  Underwriters.  This 
table  refers  to  the  most  unfavorable  cases,  namely,  when  wires  are 
covered  with  wooden  moulding  or  enclosed  in  narrow  air  spaces 
inside  the  walls  of  building. 

23.  Voltage  drop  as  a  factor  determining  the  size  of  wires. 

— The  so  called  "constant-voltage"  system  of  distribution  is  gen- 
erally used  in  electric-light  and  power  installations,  and  the  sizes 
of  distributing  wires  in  such  a  system  are  usually  determined  from 
a  prescribed  allowable  voltage  drop  (loss  of  voltage  between  the 


ELECTRIC    DISTRIBUTION    AND   WIRING. 


55 


generator  and  the  lamps).  When  more  and  more  lamps  are  put 
into  service  as  the  darkness  of  evening  comes  on  the  current 
flowing  over  the  distributing  wires  increases  and  a  larger  and 
larger  loss  of  voltage  takes  place  in  the  wires  causing  a  decrease 
of  voltage  at  the  lamps  even  though  the  voltage  at  the  generator 
be  kept  at  a  fixed  value.  Such  variation  of  voltage  at  the  lamps 
causes  an  undesirable  variation  of  brightness,  the  various  lamps 
and  motors  are  not  independent  of  each  other,  and  therefore  it  is 
necessary  to  provide  for  small  drop  of  voltage  in  the  distributing 
wires  so  as  to  obviate  large  fluctuations  of  voltage  at  the  lamps. 

TABLE  OF  CARRYING  CAPACITIES  OF  COPPER  WIRES. 

(From  National  Electrical  Code.) 

For  insulated  aluminum  wire  the  safe  carrying  capacity  is  eighty-four  per  cent, 
of  that  given  in  the  following  tables  for  copper  wire  with  the  same  kind  of  insulation. 


Brown  and 
Sharpe  Gauge. 

Sectional  Area  in 
Circular  Mils. 

Rubber 
Insulation. 
Amperes. 

Other 
Insulation. 
Amperes. 

Bare  Wires  in  Still  Air 
for  50°  F.  Rise  of 
Temperature. 

18 

1,624 

3 

5 

6.0 

16 

2,583 

6 

8 

8-5 

14 

4,107 

12 

16 

12.  1 

12 

6,530 

17 

23 

I7-I 

IO 

10,380 

24 

32 

24-3 

8 

16,510 

33 

46 

41-5 

6 

26,350 

46 

65 

58.8 

5 

33,ioo 

54 

77 

69.7 

4 

41,740 

65 

92 

83.3 

3 

52,630 

76 

no 

98.8 

2 

66,370 

90 

131 

II7.6 

I 

83,690 

107 

156 

I4O.O 

O 

105,500 

127 

185 

169.8 

oo 

133,100 

150 

220 

201.5 

ooo 

167,800 

177 

262 

240.2 

oooo 

211,600 

2IO 

312 

286.0 



400,000 

330 

500 

463-0 



600,000 

450 

680 

631.0 



1,000,000 

650 

I,  OOO 

922.0 



1,500,000 

850 

1,360 

1,250.0 



2,000,000 

I,05O 

1,670 

1,550.0 

The  lower  carrying  capacities  of  rubber-covered  wires  is  due  to  a  tendency  of 
rubber  to  deteriorate  rapidly  when  warm. 

The  question  of  voltage  drop  is  not  considered  in  this  table. 

Figure  30  represents  a  central  station  with  a  pair  of  feeders 
delivering  current  to  a  center  of  distribution  C  from  which  pairs 


56  ELECTRIC   LIGHTING. 

of  street  mains  m,  m,  m  radiate.  The  points  p,  p,  p  are 
here  called  service  points,  and  the  wires  which  lead  from  the 
service  points  into  the  houses  are  called  service  wires. 


Fig.  30. 

The  loss  of  voltage  in  the  feeders  is  usually  compensated  by 
what  is  called  feeder  control  at  the  station.  This  is  especially 
the  case  in  alternating-current  distribution  because  in  this  case 
feeder  control  is  easily  accomplished.*  Thus  we  have  constant 
voltage  at  the  center  of  distribution  C.  The  loss  of  voltage  in 
the  street  mains  and  the  loss  of  voltage  in  the  service  wires  and 
house  wires  are  not  compensated,  and  these  voltage  losses  must 
therefore  be  small  because  they  affect  the  value  of  the  voltage 
at  the  lamps.  A  total  voltage  drop  of  about  five  per  cent,  (two 
per  cent,  in  the  street  mains  and  three  per  cent,  in  the  service  and 
house  wires)  is  frequently  allowed,  although  a  greater  or  less 
drop  may  be  advisable  if  the  lamps  are  very  far  from  or  very  close 
to  the  center  of  distribution.  , 

There  are  two  causes  of  voltage  drop  in  distributing  wires, 
namely,  resistance  and  reactance,  f  Resistance  drop  of  voltage 
occurs  in  direct-current  and  alternating-current  distribution. 
Reactance  drop  of  voltage  occurs  only  n  alternating-current 
distribution. 

The  voltage  across  a  group  of  glow  lamps  is  not  appreciably 
affected  by  reactance  drop  in  the  service  wires  if  the  wires  supply 
current  to  glow  lamps  only.  The  peculiarity  of  glow  lamps  is 
that  they  are  non-inductive,  and  the  present  discussion  refers 

*  See  Art.  193,  Dynamos  and  Motors. 
t  See  Art.  112,  Dynamos  and  Motors. 


ELECTRIC    DISTRIBUTION   AND   WIRING.  57 

alike  to  alternating  and  direct  currents  when  the  receiver  is  non- 
inductive,  that  is,  when  the  receiver  has  unity  power  factor.* 

The  resistance  drop  of  voltage  along  a  distributing  line  is  equal 
to  RI  volts,  where  R  is  the  resistance  of  the  line  (both  wires) 
in  ohms  and  J  is  the  current  in  amperes  which  flows  out  in  one 
wire  and  back  in  the  other. 

The  resistance  in  ohms  of  the  two  wires  (copper)  of  a  line  is 
given  by  the  equation 

R  =  io.S~  (7) 

in  which  /  is  the  length  of  the  line  in  feet  (2l  is  the  length  of  the 
two  wires),  and  d  is  the  diameter  of  the  wire  in  mils.  One  mil  is 
equal  to  o.ooi  inch. 

The  weight  W  in  pounds  of  2/  feet  of  copper  wire  d  mils  in 
diameter  is  given  by  the  equation 

W  =  0.00000303  X  2ld?  (8) 

Proposition.  —  The  weight  in  pounds  of  the  wire  required 
to  transmit  a  given  amount  of  power  with  a  given  percentage 
loss  of  voltage  is  proportional  to  /2/E2,  where  /  is  the  distance 
from  the  generator  to  the  lamps  and  E  is  the  voltage  of  the 
generator. 

Proof.  —  Let  P  be  the  power  in  watts  to  be  delivered  by  the 
generator  and  let  p  be  the  percentage  loss  of  voltage  (actual  loss 
of  voltage  equals  pE/ioo)  .  Then  P/E  is  the  curent  in  the  line 
in  amperes,  and  R  X  P/E  is  the  loss  of  voltage  in  the  line. 
Therefore 


loo       E 

Eliminating  d2  between  equations  (7)  and  (8)  we  get  R  in 
terms  of  W  and  /;  then  substituting  this  value  of  R  inequation 
(i)  and  solving  for  W  we  have 

P/2 
TF=  0.01  308       j  (9) 

*See  Dynamos  and  Motors,  Art.  49. 


58  ELECTRIC    LIGHTING. 

Inasmuch  as  the  weight  of  the  copper  is  inversely  propor- 
tional to  E2,  according  to  equation  (9),  it  is  evident  that  a  very 
great  saving  in  copper  may  be  effected  by  using  high  voltage. 
The  permissible  voltage  at  the  lamps  is  limited,  however,  (a) 
by  the  fact  that  incandescent  lamps  cannot  be  made  to  operate 
satisfactorily  at  voltages  higher  than  about  220  volts,  and  (b) 
by  the  danger  that  is  involved  in  the  use  of  high  voltages. 

The  saving  in  copper  by  the  use  of  high  voltage,  combined 
with  the  practical  necessity  of  low- voltage  delivery,  has  led  to  the 
use  of  the  Edison  three-wire  system  as  explained  in  Art.  17. 
In  the  alternating-current  system  of  distribution  power  can  be 
transmitted  at  any  desired  high  voltage  and  cheaply  and  effi- 
ciently transformed  near  the  place  of  consumption  to  any  desired 
low  voltage.  Therefore  the  alternating-current  system  permits 
of  very  great  economy  of  copper  in  the  transmission  lines  and  does 
not  involve  any  of  the  difficulties  or  dangers  incident  to  the 
utilization  of  high  voltages  at  lamps  and  motors. 

When  the  voltage-drop  in  a  transmission  line  is  not  limited 
by  the  necessity  of  maintaining  an  approximately  constant  vol- 
tage at  the  lamps,  or  other  receiving  units,  the  size  of  wire  should 
be  determined  on  the  basis  of  economic  considerations  as  ex- 
plained in  Art.  26;  and  it  is  to  be  particularly  noted  that  the  weight 
of  copper,  demanded  by  economic  considerations,  for  the  delivery 
of  a  given  amount  of  power  is  not  proportional  to  12/E2  but  to  I  IE. 

24.  Wiring  calculations  for  a  motor  or  for  a  concentrated 
group  of  lamps. — Two  important  cases  arise  in  the  laying  out 
of  wiring  plans  in  a  constant-voltage  system,  namely,  (a)  the 
case  in  which  current  is  delivered  at  one  point  to  a  motor  or 
to  a  group  of  lamps,  constituting  what  is  called  a  concentrated 
load;  and  (b)  the  case  in  which  current  is  delivered  to  a  scattered 
group  of  lamps  or  motors,  constituting  what  is  called  a  distributed 
load. 

The  problem  of  determining  the  size  of  wire  required  to  deliver 
a  specified  amount  of  power  P  (in  watts)  to  a  concentrated  load 


ELECTRIC   DISTRIBUTION   AND   WIRING.  59 

at  a  specified  voltage  E  (at  the  lamps)  with  a  specified  drop  of 
voltage  D  in  the  line  is  solved  as  follows : 

(a)  The  current   I   is  equal  to   P/E.     Sometimes  the  current 
is  given  directly,  as  when  a  given  number  of  half -ampere  lamps, 
for  example,  are  to  be  supplied. 

(b)  The  given  voltage  drop    D    is  equal  to    RI,    so  that,    / 
being  known,  the  resistance    R   of  the  line  (both  wires)  may  be 
determined. 

(c)  Knowing  the  length    2/   of  the  wire  and  its  resistance   R, 
its  diameter  d  in  mils  may  be  calculated  with  the  help  of  equa- 
tion (7). 

The  final  result  (current  being  given)  is  expressed  by  the 
equation 

2 1. 611 
^  =  -JP  (10) 

in  which  d2  is  the  sectional  area  in  circular  mils  of  copper  wires 
required  to  deliver  /  amperes  to  a  group  of  lamps  distant  /  feet 
from  the  center  of  distribution,  D  is  the  voltage  drop,  and  E  is 
the  voltage  at  the  lamps. 

Note  i. — In  laying  out  the  wiring  for  a  house  much  time  is 
saved  by  using  wiring  charts  which  give  at  a  glance  the  solution 
of  equation  (10)  for  any  particular  case. 

Note  2. — Equation  (10)  is  frequently  used  to  determine  ap- 
proximately the  size  of  wires  required  to  deliver  a  specified  current 
to  a  distributed  load.  In  this  case  I  is  the  distance  from  the 
center  of  distribution  to  the  middle  point  of  the  distributed  load 
and  D  is  the  allowable  voltage  drop.  See  rule  2  on  page  62. 

25.  Wiring  calculations  for  distributed  loads. — When  a 
group  of  widely  distributed  lamps  is  supplied  with  current  by 
one  pair  of  service  wires,  or  when  a  group  of  widely  distributed 
customers  is  supplied  by  one  pair  of  street  mains,  we  have  what 
is  called  a  distributed  load.  The  problem  of  determining  the 
size  of  street  mains  to  supply  a  number  of  scattered  customers  is 
the  same  as  the  problem  of  determining  the  size  of  service  wires 


60  ELECTRIC    LIGHTING. 

to  supply  a  number  of  scattered  lamps.  In  the  first  case  the 
voltage-drop  between  the  center  of  distribution  and  the  various 
service  points  is  the  important  thing,  and  in  the  second  case  the 
voltage-drop  between  the  service  point  and  the  individual  lamps 
is  the  important  thing. 

In  a  distributed  load  two  kinds  of  variation  of  voltage  occur, 
namely,  (a)  the  variation  of  voltage  from  lamp  to  lamp  when  the 
number  of  lamps  in  operation  is  fixed,  and  (b)  the  variation  of 
voltage  at  any  given  lamp  as  the  number  of  lamps  in  operation 
is  increased  or  decreased. 

Concerning  the  first  type  of  variation  it  may  be  stated  in  gen- 
eral that  the  lamp  voltage  is  less  and  less  the  more  remote  the 
lamp  is  from  the  service  point,  the  most  remote  lamp  having 
always  the  lowest  voltage. 

Concerning  the  second  type  of  variation  it  may  be  stated  in 
general  that  the  voltage  at  every  lamp  falls  off  to  some  extent 
when  additional  lamps  are  turned  on,  and  rises  when  lamps 
already  in  operation  are  turned  off.  The  range  of  variation  in 
voltage  at  a  given  lamp  is  from  a  lowest  value ^when  all  the  lamps 
are  in  operation,  to  a  value  very  nearly  equal  to  the  voltage  at  the 
service  point,  when  the  given  lamp,  only,  is  in  operation.  There- 
fore, the  lamp  that  is  most  remote  from  the  service  point  is  subject 
to  the  greatest  range  of  variation  of  voltage  as  other  lamps  are 
turned  on  and  off. 

There  are  two  clearly  defined  cases  that  arise  in  the  laying  out 
of  wires  for  distributed  loads,  namely,  Case  /,  in  which  the  lamps 
supplied  by  a  given  pair  of  service  wires  are  turned  on  and  off  sepa- 
rately, and  Case  77,  in  which  all  of  the  lamps  supplied  by  a  given 
pair  of  service  wires  are  turned  on  and  off  together.  In  the  first 
case  the  wiring  must  be  laid  out  so  as  to  keep  the  voltage  varia- 
tions of  both  types  (a)  and  (b)  within  certain  limits;  and  in  the 
second  case  the  wiring  may  be  laid  out  with  reference  to  the 
limitation  of  voltage  variations  of  the  first  type  only,  that  is,  varia- 
tions of  voltage  from  lamp  to  lamp,  inasmuch  as  voltage  varia- 
tions of  the  second  type  (b)  do  not  exist  in  Case  II. 


ELECTRIC   DISTRIBUTION   AND   WIRING.  6l 

Case  I. — An  example  of  a  distributed  load  is  shown  in  Fig. 
31 .  When  all  of  the  lamps  are  in  operation  the  end  lamp,  L,  has 
the  lowest  voltage  at  any  lamp  in  the  group,  and  the  voltage  at 
this  lamp  varies  through  the  greatest  range  when  other  lamps  are 
turned  off  and  on.  Therefore,  if  the  voltage  at  the  end  lamp  is 


4 


Supply  wains 

Fig.  31. 

to  be  kept  within,  say,  three  volts  of  its  normal  value  (which 
is  the  value  when  all  the  lamps  are  in  operation)  then  the  voltage- 
drop  in  the  wires  must  not  exceed  three  volts  when  all  the  lamps 
are  in  operation. 

To  secure  a  specified  drop  out  to  the  end  lamp,  L,  when  all 
the  lamps  are  in  operation,  with  the  minimum  weight  of  copper 
in  the  wires,  the  sectional  area  of  each  portion,  a,  b,  c  and  d, 
Fig.  3 1,  of  the  wires  must  be*  proportional  to  the  square  root 
of  the  current  in  that  portion. f  Thus,  if  each  lamp  in  Fig.  31 
takes  the  same  amount  of  current,  then  the  current  values  in 
the  portions  a,  b,  c  and  d,  are  as  4  :  3  :  2  :  I,  and  the  sec- 
tional areas  of  the  respective  portions  of  the  wires  should  be  as 
1/4  :  V $  :  1/2  :  i/i  in  order  to  give  a  minimum  voltage-drop  at 
the  end  lamp,  L,  with  a  given  amount  of  copper,  or  to  give  a 

*  It  should  be  kept  in  mind  that  the  fundamental  condition  here  is  a  minimum 
amount  of  copper  for  a  given  voltage-drop.  A  minimum  amount  of  copper  for 
given  watts  lost  in  the  line  requires  the  sectional  area  of  the  wires  to  be  proportional 
to  the  current  at  each  point;  that  is,  the  number  of  circular  mils  per  ampere  must 
be  the  same  throughout  the  system  to  give  a  minimum  amount  of  copper  for  a 
given  loss  of  power  in  watts.  See  Art.  26. 

t  The  general  proof  of  this  proposition  involves  the  highly  elaborate  methods  of 
the  calculus  of  variations  and  therefore  the  proof  of  the  proposition  is  not  given  here. 


62  ELECTRIC    LIGHTING. 

minimum  amount  of  copper  for  a  specified  voltage-drop  at  the 
end  lamp,  L. 

In  laying  out  street  mains  to  supply  a  group  of  scattered  cus- 
tomers it  is  generally  advisable,  on  account  of  the  large  amount 
of  copper  involved,  to  taper  the  mains  in  steps  in  going  farther 
and  farther  from  the  center  of  distribution;  but,  as  a  rule,  the 
successive  steps  should  be  made  longer  than  the  distance  between 
adjacent  customers,  in  order  to  avoid  an  excessive  number  of 
joints  in  the  mains. 

In  laying  out  service  wires  to  supply  current  to  a  scattered 
group  of  lamps,  it  is  generally  not  advisable  to  taper  the  wires  in 
steps,  because  the  amount  of  copper  involved. may  not  be  large; 
whereas  the  expense  of  making  many  joints,  together  with  the 
expense  of  inserting  fusible  cut-outs  at  each  point  where  wires  of 
unequal  size  are  joined,  as  required  by  the  insurance  rules,  may 
be  considerable. 

Rule  i. — When  it  is  desired  to  reduce  the  size  of  a  pair  of 
street  mains  (or  service  wires)  in  steps  so  as  to  secure  the  greatest 
economy  of  copper,  the  size  of  each  portion  of  the  mains  is  deter- 
mined as  follows.  Having  given  the  total  drop  to  be  allowed  out 
to  the  end  of  the  line,  calculate  the  factor  5  from  the  equation: 

2  X  10.8  X  (a  VTi  +  b  V^.  +  c  Vis  +  >••) 
total  drop  in  volts 

in  which  a,  6,  c  •  -  -  are  the  lengths  in  feet  of  the  respective 
portions  of  the  pair  of  mains,  and  iit  i^,  i3  •  •  •  are  the  currents  in 
amperes  in  the  respective  portions.  The  sectional  areas  of  the 
various  portions  of  the  mains  in  circular  mils  are  then  equal  to 
sVii,  $V**t  sVis,  •  -  •  respectively. 

Rule  2. — When  service  wires  of  uniform  size  are  to  be  used 
for  supplying  current  to  a  scattered  group  of  lamps,  the  size  of 
the  wire  to  give  a  prescribed  drop  may  be  determined  as  follows : 
Estimate  the  distance,  L,  of  the  "center  of  gravity"  of  the  group 
of  lamps  by  the  formula: 

i'  + 1"  + 1'"  +  ... 

j_j  —  -  — — 

n 


ELECTRIC    DISTRIBUTION   AND   WIRING. 


where  I',  I",  I'",  etc.,  are  the  distances  in  feet  of  the  individual 
lamps*  from  which  the  service  point  and  n  is  the  total  number  of 
lamps  in  the  group.  ^  Then  calculate  the  size  of  the  wire  that 
would  be  required  to  supply  the  n  lamps  as  a  concentrated  group 
at  the  prescribed  total  drop  and  at  the  distance  L  from  the 
service  point. 

Case  II. — When  the  lamps  of  a  group  are  always  turned  on 
and  off  together  the  variation  of  voltage  from  lamp  to  lamp  can 
of  course  be  kept  within  bounds  by  limiting  the  voltage-drop 
between  the  service  point  and  the  end  lamp  of  the  group  as  in 
Case  I.  In  fact  a  group  of  lamps  which  is  to  be  operated  as  a 
unit  is  generally  wired  according  to  rules  I  and  2  of  Case  I ;  but 
a  special  wiring  scheme,  called  the  return-loop  scheme, f  may  be 
used  to  eliminate  voltage  variations  of  the  first  type  (see  page 
60)  in  a  group  of  lamps 
that  is  operated  as  a 
unit,  whatever  the  total 
voltage-drop  may  be. 

The  fundamental  idea 
of  thereturn-loopscheme 
may  be  seen  with  the 
help  of  Fig.  32.  The 
current  in  the  wire,  ab, 
at  any  point,  p,  is  pro- 
portional to  the  distance, 

pb,  the  lamps  being  assumed  to  be  uniformly  distributed ;  and  the 
current  at  any  point,  pf,  in  the  wire,  cd,  is  proportional  to  the  dis- 
tance p'd.  If  the  wires,  ab  and  cd,  are  tapered  so  as  to  have  sec- 
tional areas  proportional  to  thecurrent  ateach  point, then  the  value 
of  Ri  is  the  same  in  both  wires  between  any  pair  of  lamps ;  but 
Ri  is  a  drop  of  voltage  in  a  given  direction  along  one  wire  and  a 

*  If  the  lamps  are  arranged  in  subgroups  it  is  easier  to  take  /'  as  the  product  of 
the  distance  of  the  first  subgroup  times  the  number  of  lamps  in  that  subgroup, 
I"  as  the  product  of  the  distance  of  the  second  subgroup  times  the  number  of  lamps 
in  that  subgroup,  and  so  on. 

t  Sometimes  called  the  anti-parallel  scheme. 


A 


Fig.  32. 


64  ELECTRIC   LIGHTING. 

rise  of  voltage  in  the  same  direction  along  the  other  wire,  there- 
fore the  lamp  voltage  is  constant  throughout  the  group  of  lamps, 
whatever  the  total  voltage-drop  between  the  service  point  and 
the  lamps  may  be. 

The  use  of  tapered  wires  is  of  course  impracticable  and  the 
return  loop  scheme  is  always  carried  out  either  with  wires  tapered 
in  steps  or  with  wires  of  uniform  size,  usually  the  latter.  Under 

such  conditions  the  voltage 
varies  to  some  extent  from 
lamp  to  lamp  but  the  range 
of  this  variation  is  very 
much  less  than  the  total 
drop. 

The  return-loop  scheme 
of  wiring  evidently  requires 
three  wires  of  a  given 

Fig  33  length  instead  of  two,  and 

therefore  it  requires  much 

more  copper  than  the  simple  parallel  wiring  scheme  for  the 
same  total  voltage-drop.  The  advantage* of  the  return  loop 
scheme  however  is  that  a  very  large  voltage-drop  is  permissible.* 
See  page  63. 

The  return-loop  scheme  is  usually  employed  in  the  wiring  of 
churches,  lecture  halls  and  theaters,  where  the  lamps  are  either 
all  in  use  or  all  out  of  use,  or  where  the  lamps  in  certain  groups 
are  either  all  in  use  or  all  out  of  use. 

In  many  cases  the  lamps  in  a  group  are  arranged  in  a  circular 
or  reentrant  row.  In  such  a  case  the  return-loop  scheme  is 
carried  out  as  shown  in  Fig.  33,  or  as  shown  in  Fig.  34. 

Return-loop  scheme  with  wires  of  uniform  size. — When  the 
wires  used  in  the  return-loop  scheme  are  of  uniform  size  (not 
tapered)  the  middle  lamp,  p,  Fig.  35,  has  the  lowest  voltage  of 
any  lamp  in  the  group,  and  the  size  of  the  wires,  efab  and  gcd,  is 
usually  determined  with  reference  to  the  voltage-drop  between 

*  The  limit  should  be  determined  by  Kelvin's  law,  as  explained  in  Art.  26. 


ELECTRIC    DISTRIBUTION   AND   WIRING. 


the  service  point,  eg,  and  the  middle  lamp,  p.  Let  /  be  the 
total  current  delivered  to  the  group  of  lamps,  and  let  the  lamps 
be  assumed  to  be  u/iiformly  distributed  as  shown  in  Fig.  35; 


Fig.  34. 

then  the  current  in  the  element,  Ax,  is  I(X  —  x)/Xt  and  the 
voltage-drop  in  the  element,  Ax,  is  p-Ax  times  I(X  —  x)/X, 
where  p  is  the  resistance  per  unit  length  of  the  wire,  cd.  There- 
fore the  voltage-drop  along  cd  from  c  to  the  middle  lamp  is: 

r 


s*x 
Jx=0 


-  X)dx  =  ySPxi 


Also  the  voltage-drop  along   ab   from   a   to  the  middle  lamp  is 
so  that  the  total  drop  between  the  service  point,  eg,  and 


Fig.  35. 

the  middle  lamp,  p,  is  7(r' +  r"),  where  r'  is  the  resistance  of 
gc    plus  the  resistance  of  efa  ,  and   r"  is  equal  to   %pX,  where 
pX  is  the  resistance  of  one  of  the  wires,   ab  or   cd,   Fig.  35. 
6 


66 


ELECTRIC   LIGHTING. 


Rule  3. — To  give  a  prescribed  voltage-drop  between  the  ser- 
vice point  and  the  middle  lamp  of  a  row,  which  is  connected 
according  to  the  return-loop  scheme,  make  the  wire  of  such  size 
that  the  total  current  delivered  to  the  group  of  lamps  would  give 
the  prescribed  drop  over  a  length  /'  +  /"  of  the  wire,  where  I'  is 
the  sum  of  the  distances,  gc  and  efa,  in  Fig.  35,  and  I"  is  three 
fourths  of  the  distance  ab. 

Modifications  of  Cases  I  and  II. — Every  practical  case  of 
wiring  in  the  constant-voltage  system  of  distribution  can  be 
treated  as  a  slight  modification  of  Cases  I  and  II  above  described. 
Thus  Fig.  36  shows  two  groups  of  lamps  each  exactly  like  the 


WWW 


WWW 


Fig.  36. 


Fig.  37. 


single  group  in  Fig.  31  ;  and  Fig.  37  shows  a  combination  of  Figs. 
31  and  32,  that  is,  the  portion,  pa,  of  the  group  of  lamps  in 
Fig.  37  is  arranged  in  conformity  with  Fig.  31  and  the  portion, 
pb,  is  arranged  in  accordance  with  the  return  loop  scheme. 

26.  The  economic  balance  between  loss  of  power  and  the  cost 
of  copper  in  the  distribution  of  electric  current.—  The  original 


ELECTRIC    DISTRIBUTION    AND   WIRING.  67 

cost  of  erection  of  a  distributing  line  consists  of  two  nearly  inde- 
pendent parts,  namely  (a)  the  cost  of  the  copper  and  (b)  the  cost 
of  poles,  cross-arms,  p^ins  and  insulators  and  the  cost  of  erection. 
That  is  to  say,  even  if  one  were  to  double  the  size  of  wires  to  be 
used  the  cost  of  item  (b)  would  not  be  increased  to  any  consider- 
able extent.  The  disadvantage  of  using  large  wires  lies,  there- 
fore, almost  wholly  in  the  annual  "charge,"  including  interest  on 
the  cost  of  the  wire,  depreciation  of  the  wire,  and  taxes  thereon. 
The  advantage*  of  using  large  wires,  on  the  other  hand,  lies  in 
the  decreased  loss  of  power  in  the  wires.  Therefore,  the  most 
economical  size  of  wire  is  that  for  which  the  additional  annual 
"charge"  on  a  larger  wire  would  exceed  the  annual  value  of  the 
power  saved  by  the  use  of  the  larger  wire,  or,  in  other  words,  the 
most  economical  size  of  wire  is  that  for  which  the  sum  of  the 
annual  "charge"  on  the  total  copper  plus  the  annual  value  of  the 
power  lost  in  the  wires  is  a  minimum. 

The  economic  balance  between  loss  of  power  and  cost  of  copper 
always  leads  to  a  definite  number  of  circular  mils  of  sectional 
area  of  wire  per  ampere  of  current,  without  regard  to  the  voltage 
or  to  the  distance  of  transmission. 

Electric  power  is  to  be  supplied  for  h  hours  each  year  to  a 
customer.  The  cost  of  power  at  the  switchboard  is  p  dollars  per 
kilowatt-hour,  the  cost  of  copper  is  c  dollars  per  pound,  and  the 
interest  charge  on  invested  capital  (including  a  small  percentage 
to  cover  the  depreciation  of  copper  wires  and  taxes)  is  t  per  cent, 
per  annum.  It  is  required  to  find  the  sectional  area  of  the  cop- 
per wire  in  circular  mils  per  ampere  of  current  on  the  condition 
that  any  increase  in  the  amount  of  copper  would  effect  a  saving 
of  power  of  which  the  annual  value  would  be  less  than  the  interest 
on  the  cost  of  the  additional  copper.  Let  2/  be  the  length  of 
the  wire  in  feet  (equal  to  twice  the  length  of  the  line) ,  s  its  sec- 
tional area  in  circular  mils,  R  its  resistance  in  ohms,  W  its 

*  It  is  to  be  kept  in  mind  that  we  are  not  here  considering  the  fact  that  in  the 
constant- voltage  system  the  wires  must  be  large  enough  to  limit  the  voltage-drop, 
as  explained  on  pages  54-66. 


68  ELECTRIC   LIGHTING. 

weight  in  pounds,  and    /    the  current  in  amperes.     Then    R  = 

10.8  X  2l/s   so  that  the  lost  power  in  kilowatts  is    —  '-  ---  J2, 

1,000  ^ 

and  the  annual  loss  of  energy  is          ---  Ph   kilowatt-hours,   of 

i  ,000  «y 

which  the  value  at  p  dollars  per  kilowatt-hour  is    —  -  —  Pph 

dollars  per  year.  On  the  other  hand  W  =  0.00000303  X  2ls 
pounds,  of  which  the  cost  is  o.ooooo6o6/sc  dollars,  the  interest 
on  this  cost  is  o.ooooooo6o6/sc/  dollars  per  year,  and  the 

quantity  to  be  made  a  minimum  by  choosing    s    is 


1,0005 

+  o.ooooooo6o6/sc/.      Differentiating  this  expression  with  respect 
to   5   and  placing  the  differential  coefficient  equal  to  zero  gives: 

—  -      —  ^  •  Pph  +  o.ooooooo6o6/c/  =  o 

1  ,00052 

from  which   /   cancels  out,  and  we  find  : 

pt 

f 
ct 


s  ( 

-  —  circular  mils  per  ampere  =  597  Af 
j.  » 


or 

IM 

(n) 

The  meanings  of  the  symbols,  s,  /,  h,  p,  c  and  t,  are  specified 
above.  When  the  delivered  current,  I,  is  not  constant,  the 
average  value  of  the  current  must  not  be  used,  but  the  square- 
root-of-the-average-value-of-the-square  should  be  used  in  equa- 
tion (n). 

Example  I. — The  cost  of  power  at  the  switchboard  of  an 
electric-power  station  is  1.6  cents  per  kilowatt-hour  (p  =  0.016), 
the  interest  on  invested  capital  is  5  per  cent.,  and  the  annual 
depreciation  and  taxes  is  three  per  cent.  (/  =  8),  the  cost  of  cop- 
per wire  is  1 6  cents  per  pound  (c  =  0.16),  and  a  current  of  200 
amperes  is  delivered  to  a  customer  for  1,000  hours  each  year. 
Considerations  of  economy  would  lead,  under  these  conditions, 


ELECTRIC   DISTRIBUTION   AND   WIRING.  69 

to  the  use  of  transmission  wires  650  mils  in  diameter,  whatever 
the  distance  of  the  customer  from  the  station  may  be. 

If  the  distance  from  the  station  to  the  consumer  is  538  feet, 
then  the  total  length  of  wire  is  1 ,076  feet,  its  resistance  is  0.0275 
ohm,  and  the  voltage-drop  with  200  amperes  is  5.5  volts.  That 
is,  if  current  is  to  be  supplied  to  the  customer  at  1 10  volts,  the 
size  of  wire  required  on  the  basis  of  a  5  per  cent,  drop  of  voltage 
is  the  same  as  the  size  of  the  wire  required  to  give  an  economic 
balance  between  the  loss  of  power  and  the  cost  of  copper  under 
the  specified  conditions.  If  the  distance  is  greater  than  538  feet, 
then  considerations  of  economy  would  give  a  smaller  wire  than 
would  be  required  by  a  5  per  cent,  drop  in  voltage;  and,  if  the 
distance  is  less  than  538  feet,  then  considerations  of  economy 
would  give  a  larger  wire  than  would  be  required  by  a  5  per  cent, 
drop  in  voltage. 

Example  2. — Cost  of  power,  rate  of  interest  and  cost  of  cop- 
per being  the  same  as  in  example  I,  it  is  required  to  find  the 
most  economical  size  of  wire  for  carrying  100  amperes  for  400 
hours  each  year  and  300  amperes  for  600  hours.  The  average 
square  of  the  current  is 

(ioo2  X  400)  +  (3002  X  600) 

177 -  =  58, ooo  amperes-squared 

and  the  square-root-of-average-square  is  241  amperes.  There- 
fore using  h  =  400  +  600  hours  and  /  =  241  amperes  in  equa- 
tion (n),  we  have  5  =  509,200  circular  mils,  or  the  diameter  of 
the  wire  must  be  713  mils. 

Kelvin's  law. — Dependence  of  total  weight  of  copper  on  voltage 
of  delivery  and  distance  of  customer  from  station. — A  given  amount 
of  power,  P,  is  to  be  delivered  to  a  customer  at  a  distance,  /, 
from  the  station  and  at  a  voltage,  E.  The  current  is  P/E  so 
that  from  equation  (10)  we  have: 


•  597£  N^F 


70  ELECTRIC   LIGHTING. 

which,     substituted    in    the    formula     W  =  0.00000303  X  2/5, 
gives  : 


W  =  0.0036I8P-  (12) 

which  shows  that  the  amount  of  copper  required  by  economic 
considerations  is  proportional  to  the  distance,  /,  and  inversely 
proportional  to  the  voltage  of  delivery. 

It  is  important  to  note  the  difference  between  equations  (9) 
and  (12).  To  deliver  a  specified  amount  of  power  requires  a 
weight  of  copper  which  is  proportional  to  /2/£2  when  the  per- 
centage voltage  drop  is  fixed  whereas  it  requires  a  weight  of 
copper  proportional  to  l/E  if  maximum  economy  is  the  ruling 
condition. 

Limitations  of  Kelvin's  law.  —  The  economic  balance  between 
the  loss  of  power  in  transmission  wires  and  the  cost  of  copper 
was  first  pointed  put  by  Lord  Kelvin,  and  the  condition  ex- 
pressed by  equation  (12)  is  sometimes  called  Kelvin's  law  of 
economy.*  In  the  derivation  of  equation  (12)  it  was  assumed, 
first,  that  the  cost  of  poles,  cross-arms  and  'pins,  and  the  cost 
of  erection  of  the  pole  line  are  the  same  whatever  the  size  of 
the  wire  may  be,  and  second,  that  the  cost  of  the  wire  is  so  much 
per  pound  irrespective  of  size.  The  first  assumption  is  approxi- 
mately true  only  for  wires  of  moderate  weight.  For  very  heavy 
wires  the  supporting  structure  must  be  very  strong  and  there- 
fore expensive.  The  second  assumption  is  approximately 
true  only  for  bare  wires.  For  insulated  wires  the  cost  per 
pound  varies  considerably  with  the  size  of  the  wire. 

27.  Corona  formation  as  a  factor  determining  the  size  of 
wires.  —  When  the  voltagef  between  two  line  wires  is  increased 
more  and  more  a  point  is  ultimately  reached  where  the  air  in 

*  A  very  full  discussion  of  Kelvin's  law  is  given  by  Dr.  F.  A.  C.  Perrine  in  his 
book  entitled  Conductors  for  Electric  Distribution,  pages  161-178  (D.  Van  Nostrand, 

1903)- 

t  This  article  refers  to  alternating  voltages.  Direct  voltages  exceeding  a  few 
thousand  volts  never  occur  in  ordinary  engineering  practice. 


ELECTRIC   DISTRIBUTION   AND   WIRING.  Ji 

the  neighborhood  of  the  wires  breaks  down  and  we  have  what 
is  called  the  corona,  a  faint  bluish  glow  surrounding  the  wires. 
A  sufficiently  high  ^voltage  causes  the  complete  break-down  of 
the  air  insulation  and  the  formation  of  an  electric  arc  from 
wire  to  wire. 

The  corona  may  be  easily  shown  as  follows:  Two  very  fine 
wires  (line  wires)  are  supported  on  glass  rods  at  a  distance  of 
6  or  8  inches  apart  in  a  very  dark  room,  and  the  wires  are  con- 
nected to  the  secondary  of  a  good-sized  induction  coil  the 
primary  of  which  is  connected  to  alternating  current  supply 
mains.  A  much  smaller  induction  coil  will  suffice  if  its  primary 
is  excited  by  direct  current  using  a  Wehnelt  interrupter. 

By  using  two  pairs  of  "line  wires,"  one  pair  much  finer  than 
the  other,  and  connecting  both  pairs  to  the  induction  coil  simul- 
taneously it  can  be  shown  that  the  corona  starts  on  the  finer 
wires  more  easily  (at  a  lower  voltage)  than  on  the  coarser  wires. 
Indeed  the  approximate  voltage  E  required  to  start  an  electrical 
breakdown  of  the  air  between  two  line  wires  is: 

/ 2S\ 

E  =  150^  •  logio  1  -7-  I  (13) 


in  which  d  is  the  diameter  of  the  line  wires  in  mils,  and  S  is  the 
distance  of  the  wires  apart  center  to  center  in  mils.  Thus 
about  55,000  volts  is  required  to  start  the  corona  on  wires 
125  mils  in  diameter  and  4  feet  apart  center  to  center;  and  about 
3,000  volts  is  required  to  start  the  corona  on  wires  6  mils  in 
diameter  and  6  inches  apart  center  to  center.  In  the  case  of 
very  fine  wires,  however,  the  corona  is  limited  to  the  region 
very  near  to  the  wires  unless  the  voltage  greatly  exceeds  the 
corona-starting  voltage. 

The  only  cases  in  practice  where  corona  formation  occurs 
is  near  the  very  high-voltage  terminals  of  transformers  and 
on  very  high-voltage  transmission  lines,  and  in  such  cases  d 
and  5  are  both  made  large  enough  to  give  a  corona-starting 
voltage  about  two  times  as  great  as  the  voltage  which  is  used. 


ELECTRIC    LIGHTING. 


Thus  half -inch  line  wires  would  have  to  be  25  inches  apart 
center  to  center  to  require  a  corona-starting  voltage  of  150,000 
volts,  and  therefore  half -inch  wires  25  inches  apart  would  be 
suitable  for  about  75,000  volts;*  or  if  the  distance  apart  of 
the  wires  is  fixed  at  25  inches  it  would  not  be  allowable  to  use 
wires  much  smaller  than  500  mils  in  diameter  on  a  75,ooo-volt 
transmission  line. 

A  very  full  discussion  of  electrical  stresses  and  a  derivation  of 
equation  (13)  are  given  in  Appendix  A. 

28.  Pole  line  insulation. — When  the  voltage  between  two 
line  wires  is  distinctly  less  than  that  required  to  cause  an  elec- 
trical break-down  of  the  air  in  the  neighborhood  of  the  wires, 
the  leakage  of  current  through  the  air  from  wire  to  wire  is  entirely 
negligible;  the  only  appreciable  leakage  of  current  is  at  the 
supporting  insulators  and  through  branches  of  trees  and  other 
objects  which  happen  to  touch  the  wires. 

If  the  insulators  are  made  of  glass  or 
thoroughly  vitrified  porcelain  the  leakage  of 
the  current  through  the  .material  of  the  in- 
sulator is  always  negligible,  unless  the  insula- 
tor is  ruptured,  but  the  leakage  of  current 
over  the  surface  of  the  insulator  may  be  con- 
siderable. This  leakage  over  the  surface  of 
an  insulator  is  reduced  to  a  minimum  by 
designing  the  insulator  so  that  the  leakage 
path  measured  along  the  surface  (see  dotted 
line  in  Fig.  38)  may  be  as  long  as  possible 
and  so  that  a  portion  of  the  surface  may  be  shielded  from  rain  or 
mist.  This  is  accomplished  by  making  a  series  of  deep  grooves 
around  the  bottom  of  the  insulator  as  shown  by  the  dotted  lines 
at  the  base  of  the  insulator  in  Fig.  27.  Figure  38  shows  a  typical 
high-voltage  insulator.  This  type  of  insulator  is  deficient  in 

*  An  alternating  voltage  of  75,000  effective  value  has  a  maximum  value  of  about 
105,000  volts  on  the  peak  of  the  wave  so  that  a  corona-starting  voltage  of  150,000 
volts  on  a  7 5,000- volt  transmission  line  would  mean  a  "factor  of  safety"  of  about  3/2. 


Fig.  38. 


ELECTRIC    DISTRIBUTION   AND   WIRING.  73 

mechanical  strength  and  a  more  recent  type  called  a  strain  in- 
sulator is  shown  in  Fig.  39.  The  strain  insulator  is  used  as 
a  link  in  a  chain  which  supports  the 
transmission  wire  as  shown  in  Fig.  40. 
The  strength  of  an  insulator  to  with- 
stand high  voltage  without  rupture  has 

Fig.  39. 

nothing  directly  to  do  with  its  insula- 
tion resistance,  in  the  same  way,  that  the  strength  of  a  porous 
earthenware  jar  to  withstand  hydraulic  pressure  without  bursting 
has  nothing  directly  to  do  with  the  facility  with  which  the  porous 
walls  of  the  jar  permit  the  water  to  flow  through  them.  There- 
fore the  most  important  test  of  a  high-voltage  insulator  is  the 
break-down  test.  In  this  test  the  insulator  pin  and  a  wire  tied 
around  the  insulator  are  connected  to  the  secondary  of  a  high- 
voltage  testing  transformer  and  the  voltage  is  raised  to  the 
desired  value.  In  testing  a  lot  of  insulators 
which  are  to  be  used  the  test  voltage  is  run 
up  to  I  Y%  or  2  times  the  voltage  which  the 
insulators  are  to  stand  in  service. 

Wires  on  pole  lines  are  provided  with  insu- 
lating covering  only  when  it  is  desired  to  re- 
duce the  risk  of  accidental  momentary  contacts. 
Thus  the  moderately  high -voltage  lines  (2,200 
to  5,000  volts)  which  supply  arc  lamps  on 
city  streets  usually  have  insulating  covering. 
The  wires  of  high-voltage  transmission  lines 

Fig.  40. 

are  always  bare  because   any  ordinary  insu- 
lating covering  would  be  entirely  inadequate. 

29.  Insulation   of   underground,   house    and   station   wires. 

— In  the  installation  of  underground,  house  and  station  wires, 
two  things  are  kept  in  view,  namely,  (a)  the  insulation  of  the 
wires  and  (b)  the  protection  of  the  wires  from  mechanical  injury. 
It  is  especially  important  to  use  an  absolutely  waterproof  insula- 
tion such  as  rubber  or  lead  encased  fiber;  and  the  most  satis- 


74  ELECTRIC    LIGHTING. 

factory  mechanical  protection  is  that  which  is  afforded  by  an  iron 
pipe  or  by  a  vitrified  clay  conduit  laid  in  concrete  or  built  in 
the  floor  and  walls  of  a  building. 

30.  National  Electrical  Code. — Rules  governing  the  installa- 
tion of  electrical  apparatus  of  all  kinds  have  been  formulated 
by  a  national  conference*  with  the  object  of  minimizing  fire  risks 
and  risks  of  personal  injury.  These  rules  are  published  in 
convenient  form  -and  sold  at  a  nominal  price  by  the  National 
Board  of  Fire  Underwriters!  under  the  title  "The  National 
Electrical  Code." 

The  rules  and  requirements  which  constitute  the  National 
Electrical  Code  are  classified  in  the  1911  edition  as  follows: 

Class  A .     Rules  applying  to  stations  and  dynamo  rooms. 

Class  B.      Rules  applying  to  outside  work. 

Class  C.  Rules  applying  to  inside  work  (wiring  and  lamp  and 
motor  installations). 

Class  D.  Rules  applying  to  fittings,  materials  and  details  of 
construction. 

Class  E.  Miscellaneous.  Rules  applying  to  telephone  and 
telegraph,  fire  and  burglar  alarms,  etc. 

Class  F.     Marine  work. 

Classes  A,  B,  C  and  E  are  issued  in  one  volume  for  general 
distribution,  and  Classes  D  and  F  are  issued  in  another  volume 
which  may  be  obtained  from  the  National  Board  by  any  one 
interested  in  the  special  rules  contained  therein.  Contractors 
and  station  managers  are  specially  interested  in  the  list  of 

*  The  following  is  a  list  of  the  Associations  composing  this  National  Conference: 
American  Institute  of  Architects,  American  Institute  of  Electrical  Engineers, 
American  Society  of  Mechanical  Engineers,  American  Institute  of  Mining  Engi- 
neers, American  Street  Railway  Association,  Associated  Factory  Mutual  Fire 
Insurance  Companies,  Association  of  Edison  Illuminating  Companies,  International 
Association  of  Fire  Engineers,  International  Association  of  Municipal  Electricians, 
National  Board  of  Fire  Underwriters,  National  Electric  Light  Association,  National 
Electrical  Contractors'  Association  and  Underwriters'  National  Electric  Association. 

A  brief  history  of  the  development  of  the  National  Electrical  Code  is  given  by 
C.  E.  Skinner,  Electric  Journal,  Vol.  II,  pages  262-265,  January.  1906. 

t  General  agency,  34  Nassau  St.,  New  York  City. 


ELECTRIC   DISTRIBUTION   AND   WIRING. 


75 


"approved"  fittings  which  is  issued  semi-annually  by  the  Na- 
tional Board  for  general  distribution. 

WEIGHTS  AND  RESISTANCES  OF  COPPER  WIRE. 
Brown  and  Sharpe  Gauge. 


Gauge 
Num- 
bers. 

Diameters 
in  Mils  =  d. 

Areas  in  Cir- 
cular Mils 
=  ^3. 

Weights. 

Resistances  per  1,000  Feet  in 
International  Ohms. 

Per  i.  ooo 
Feet. 

Per  Mile. 

At  60°  F. 

At  75°  F. 

oooo 
ooo 
oo 

0 

I 

460 
410 
365 
325 
289 

2II,6OO 
168,100 
133,225 
105,625 
83,521 

64I 
509 
403 
320 

253 

3,382 
2,687 
2,129 

1,688 
i,335 

.04811 
.06056 
.07642 
.09639 
.1219 

.04966 
.06251 
.07887 
.09948 
.1258 

2 

3 

4 

6 

258 
229 
204 
182 
162 

66,564 

52'!4! 
41,616 

33,124 

26,244 

202 

'59 
126 

100 

79 

1,064 
838 
665 

529 
419 

.1529 
.1941 
.2446 
.3074 
.3879 

•1579 
.2004 

.2525 
.3172 
.4004 

9 

10 

II 

144 
128 
II4 
102 
91 

20,736 
16,384 
12,996 
10,404 
8,281 

63 
50 
39 
32 
25 

33i 
262 
208 
166 
132 

.491 
.6214 
.7834 
.9785 
1.229 

.5067 
.6413 
.8085 
1.  01 

1.269 

12 

13 
14 
15 

16 

Si 
72 
64 

57 
5i 

6,56i 
5,184 
4,096 

3,249 
2,601 

20 

15.7 

12.4 
9.8 
7-9 

105 
83 
65 
52 
42 

1-552 
1.964 
2.485 
3-133 
3-9H 

1.601 
2.027 
2.565 
3-234 
4.04 

17' 

18 

19 
20 

21 

45 

$ 
Si 

2,025 
i,  600 
1,296 
1,024 
812.3 

6.1 
4.8 
3-9 
3-i 

2-5 

i526 

20.7 
16.4 
13 

5.028 
6.363 
7-855 
9-942 
12.53 

5.189 
6.567 
8.108 
10.26 
12.94 

22 
23 
24 

3 

25-3 

22.6 
20.1 
17.9 
15-9 

640.1 
510.8 
404 
320.4 
252.8 

1.9 
1-5 

1.2 

•97 

•77 

IO.2 

8.2 

6.5 

5-i   » 
4 

15-9 

'9-93 
25.2 

31-77 
40.27 

16.41 
20.57 
26.01 

32.79 
41.56 

27 
28 
29 
30 
31 

14.2 
12.6 

"•3 
IO 

8.9 

2OI.6 

158.8 
127.7 

100 

79.2 

.61 
.48 
•39 
•3 
.24 

32 
2-5 

2 

1.6 
1.27 

5°-  49 
64.13 

79.73 
101.8 
128.5 

52.11 
66.18 
82.29 
105.1 

132.7 

32 

33 
34 

\ 

8 
7i 
6.3 
5.6 

5 

64 

50-4 
39.7 
31.4 
25 

.19 
•15 

.12 

•095 
.076 

i.  02 
.81 
•63 
•  5 
•4 

I59-I 

202 

256.5 
324.6 
407.2 

164.2 
208.4 
264.7 

335-1 
420.3 

76  ELECTRIC   LIGHTING. 

This  table  is  based  on  a  resistance  of  10.51  ohms  per  mil-foot  at  75°  F.,  a  temper- 
ature coefficient  of  resistance  of  0.0022  per  degree  Fahrenheit,  and  a  density  of 
3.03  X  io~6  pound  per  mil-foot,  or  555  pounds  per  cubic  foot. 

According  to  the  Report  of  the  Standardization  Committee  of  the  American 
Institute  of  Electrical  Engineers*  it  is  commercially  feasible  to  supply  annealed 
copper  for  electric  wires  and  cables  having  a  resistance  not  greater  than  102  per 
cent,  of  the  "annealed  copper  standard,"  and  hard-drawn  copper  having  a  resist- 
ance not  exceeding  105  per  cent,  of  the  "annealed  copper  standard."  The  an- 
nealed copper  standard  is  10.36  ohms  per  mil-foot  at  20°  C. 

Aluminum. — Resistances  in  above  table  are  to  be  multiplied  by  1.61  for  alumi- 
num wire. 

Weights  in  above  table  are  to  be  multiplied  by  0.30  for  aluminum  wire. 

Iron  and  Steel. — Resistances  in  above  table  are  to  be  multiplied  by  about  7  for 
iron  and  steel  wires. 

Weights  in  above  table  are  to  be  multiplied  by  0.876  for  iron  and  steel  wires. 

IMPORTANT   BOOKS   ON   WIRING. 

National  Electrical  Code,  National  Board  of  Fire  Underwriters. 
Standard  Tables  for  Electric  Wiremen,  C.  P.  Poole,  McGraw-Hill  Book  Co. 
Electric  Light  Wiring,  C.  E.  Knox,  McGraw-Hill  Book  Co. 
Conductors  for  Electrical  Distribution,  F.  A.  C.  Perrine. 

Electrical  Transmission  of  Energy,  A.  V.  Abbott,  Van  Nostrand.     This  book  con- 
tains a  very  full  discussion  of  pole  lines  and  of  underground  conduits  and  cables. 

*  Paragraph  260  of  Rules  as  adopted  on  June  27,  1911.  See  Proceedings  of 
Institute  for  August,  1911,  page  1942. 


CHAPTER   III. 

ALTERNATING-CURRENT   LINES. 

31.  Direct-current  and  alternating-current  calculations  com- 
pared.— Kelvin's  law  of  economy  (see  Art.  26)  applies  without 
distinction  to  direct  current  and  to  alternating  current  when  the 
value  of  the  current  is  given.  If  an  amount  of  power  P  is  to  be 
delivered  at  voltage  E,  the  current  is  equal  to  P/E  in  the  case 
of  direct-current  transmission,  but  the  current  is  equal  to  P/(pE) 
in  the  case  of  alternating-current  transmission,  where  p  is  the 
power  factor  of  the  receiver. 

When  the  size  of  wires  is  to  be  determined  on  the  basis  of  a 
prescribed  voltage  drop  (see  Arts.  23-25)  then  alternating-cur- 
rent calculations  differ  from  direct-current  calculations,  although 
the  direct-current  method  (which  refers  only  to  resistance  drop  of 
voltage)  is  approximately  correct  for  alterating-current  wiring  when 
the  power  factor  of  the  receiver  is  nearly  unity. 

This  chapter  refers  to  alternating-current  wiring  calculations  on 
the  basis  of  a  prescribed  voltage  drop  but  when  the  power  factor  of 
the  receiver  is  not  equal  to  unity. 

The  methods  of  this  chapter  give  very  accurate  results  for 
transmission  distances  up  to  ten  or  twenty  miles  at  the  usual 
alternating-current  frequencies,  but  they  give  only  approximate 
results  for  very  long  transmission  lines. 

On  a  very  long  transmission  line  the  effects  of  line  capacity 
must  be  taken  into  account  in  precise  calculations.*  The  effect 
of  line  capacity  is  primarily  to  cause  a  difference  between  the 
current  which  flows  into  the  line  at  the  generator  end  and  the 
current  which  flows  out  of  the  line  at  the  receiver  end.  This 

*  The  simplest  rigorous  discussion  of  the  alternating-current  transmission-line 
problem  is  that  which  is  given  in  Chapter  V  (pages  116-153)  of  Electric  Waves,  by 
W.  S.  Franklin,  The  Macmillan  Co.,  1909.  This  discussion  is  easily  followed 
because  the  geometric  and  physical  features  of  the  problem  are  kept  in  view,  and 

77 


78  ELECTRIC    LIGHTING. 

difference  is  called  the  charging  current  of  the  line.     The  effects 
of  capacity  are  ignored  in  this  chapter. 

32.  Resistance  drop  and  reactance  drop  on  a  line.* — Figure 
41  is  a  clock  diagram  in  which  the  line  01  represents  the  current 
flowing  through  the  transmission  line  and  through  the  receiving 
circuit,  and  the  line  E\  represents  the  voltage  across  the  receiving 
circuit,  6  being  the  phase  difference  between  EI  and  /  as 


shown.  Let  r  be  the  resistance  and  x  the  reactance  of  the  line. 
Then  rl  is  the  resistance  drop  on  the  line  and  it  is  in  phase  with  / 
(parallel  to  I  in  the  clock  diagram),  and  xl  is  the  reactance 
drop  on  the  line  and  it  is  90°  ahead  of  /  in  phase.  The  generator 
voltage  EQ  is  equal  to  the  vector  sum  of  EI,  rl  and  xl. 

The  numerical  difference  between  £0  and  EI  is  usually  called 
simply  the  line  drop.  It  is  evident  from  Fig.  41  that  the  line 
drop  is  a  complicated  function  of  /,  0,  EI,  r  and  x. 

33.  Line  resistance. — The  resistance  of  a  wire  for  alternating 
current  is  in  nearly  all  practical  cases  sensibly  equal  to  the  resist- 
ance of  the  same  wire  for  direct  current.  When  the  wire  is  very 
large,  however,  or  when  the  frequency  is  very  high,  the  alternating 

because  the  solution  is  expressed  in  terms  of  familiar  exponential  functions.  These 
exponential  functions  (as  they  appear  in  the  solution  of  this  problem)  are  the  so- 
called  hyperbolic  sines  and  cosines;  but  it  is  distinctly  misleading  to  call  them  such, 
because  to  do  so  is  to  convey  the  impression  that  the  mathematics  of  the  problem 
involves  something  which  is  entirely  unfamiliar  and  new,  which  is  distinctly  not 
the  case;  and  every  table  of  logarithms  is  in  effect  a  table  of  hyperbolic  sines  and 
cosines  provided  one  ignores  these  names  and  looks  at  the  simple  facts. 

*  This  matter  is  discussed  in  Dynamos  and  Motors,  Art.  112.  A  general  state- 
ment is  repeated  here  for  the  sake  of  clearness. 


ALTERNATING   CURRENT   LINES. 


79 


current  flows  chiefly  through  the  surface  layers  of  the  wire,  and 
the  resistance  of  the  wire  is  very  perceptibly  larger  for  alternating 
current  than  for  direct  current.  This  effect  is  called  the  skin 
effect* 

34.  Line  reactance.  —  The  reactance  of  a  transmission  line 
(outgoing  and  returning  wires  side  by  side)  depends  upon  the  size 
of  the  wires  and  upon  their  distance  apart  center  to  center,  and 
it  is  proportional  to  the  length  of  the  line  and  to  the  frequency.! 


RESISTANCE  AND  REACTANCE  OF  ONE  MILE  OF  WIRE 
OF   TRANSMISSION   LINE). 


MILE 


Reactance  in  Ohms. 

Size  of 
Wire  B. 

Resist- 

At  60  Cycles  per  Sec. 

At  125  Cycles  per  Sec. 

&S. 
Gauc*e 

Ohms. 

Wires 

Wires 

Wires 

Wires 

Wires 

Wires 

\-7<XUgC. 

12  Inches 

18  Inches  « 

24  Inches 

12  Inches 

18  Inches 

24  Inches 

Apart. 

Apart. 

Apart. 

Apart. 

Apart. 

Apart. 

oooo 

•259 

.508 

•557 

•591 

.06 

•17 

1.23 

ooo 

.324 

•523 

•573 

.607 

.09 

.20 

1.26 

oo 

.412 

•534 

.588 

.618 

.12 

•23 

.29 

o 

.519 

•550 

.603 

.633 

•IS 

.26 

•32 

i 

•655 

.565 

.614 

.648 

.18 

.28 

•35 

2 

.826 

•  580 

.629 

.663 

.21 

.31 

•38 

3 

1.041 

•591 

.644 

.674 

.24 

•34 

.41 

4 

1-313 

.606 

.656 

.690 

.26 

•37 

•44 

5 

1.656 

.620 

.670 

.704 

•30 

.40 

•47 

6 

2.088 

.633 

.685 

.720 

•32 

•43 

•49 

7 

2.633 

.647 

.700 

•730 

•35 

.46 

•52 

8 

3-320 

.662 

.712 

.742 

•38 

.48 

•55 

9 

4,186 

•677 

.727 

.761 

.41 

•51 

•58 

10 

5.280 

.688 

.742 

.776 

.44 

•54 

.62 

The  following  table  gives  the  resistance  and  reactance  per  half 
mile  of  transmission  line,  using  copper  wires. 

35.  Calculation  of  a  single-phase  transmission  line  to  give  a 
specified  line  drop.J — A  single-phase  transmission  line  is  to 

*  See  Ernest  Merritt,  Physical  Review,  Vol.  V,  pages  47-60,  July,  1897. 

f  Derivations  of  the  formulas  for  line  reactance  and  line  capacity  are  given  in 
Electric  Waves,  by  W.  S.  Franklin,  Appendix  A. 

J  A  good  discussion  of  the  exact  theory  of  line  drop  on  a  long  alternating-current 
transmission  line  is  given  on  pages  141-153  of  Franklin's  Electric  Waves.  The 
Macmillan  Company,  1909. 

A  series  of  papers  on  the  exact  calculation  of  alternating-current  transmission 
line  problems,  by  W.  F.  Miller,  is  given  in  the  General  Electric  Review,  Vol.  XIII, 


80  ELECTRIC   LIGHTING. 

deliver  a  prescribed  amount  of  power  P  at  a  prescribed  electro- 
motive force  EI  to  a  receiving  circuit  of  which  the  power  factor, 
cos  0,  is  given;  the  line  drop,  frequency,  length  of  time,  and  dis- 
tance apart  of  wires  being  given. 

The  generator  voltage  Eo  is  equal  to  the  sum  (numerical  sum) 
of  EI  and  line  drop. 

The  full  load  current  /  is  found  from  the  relation  EI/  cos  0 
equals  P. 

The  component  of  EI  parallel  to  /  is  EI  cos  0,  and  the  com- 
ponent of  EI  perpendicular  to  /  is  EI  sin  6. 

By  treating  the  problem  first  as  a  direct-current  problem,  the 
approximate  resistance  r'  of  the  line  is  found  from  the  relation 
r'l  equals  line  drop.  From  this  approximate  resistance  and  the 
known  length  of  the  line,  the  approximate  size  of  the  wire  and 
the  line  reactance  x  may  be  found  from  the  table ;  and  since  the 
line  reactance  varies  but  little  with  the  size  of  the  wire,  the  value 
of  x  need  not  be  further  approximated. 

The  component  of  Eo  parallel  to  /  is  EI  cos  6  +  rl,  where  r 
is  the  true  resistance  of  the  line,  and  the  component  of  E0  per- 
pendicular to  /  is  EI  sin  8  +  xl.  Therefore 

E02  =  (Ei  cos  0  +  rl)2  +  (Ei  sin  6  +  xl)2 
or  

l/Eo2  -  (Ei  sin  6  +  xl)2  -  El  cos  0 
r  =  -  —f~  (0 

From  this  equation  the  true  line  resistance    r    may  be  found 
and  thence  the  correct  size  of  wire. 
Example: 

Ei  =  20,000  volts. 

P  =  i  ,000  kilowatts. 

cos  0  =  0.85  =  power  factor  of  receiving  circuit. 

Eo  =  23,000  volts,  or  line  drop  =  3,000  volts. 

frequency  =  60  cycles  per  second. 

pages  177-181,  220-227,  264-267,  and  326-330,  April  to  July,  1910.  These  papers 
refer  especially  to  three-phase  lines.  A  table  of  hyperbolic  functions  is  published 
in  a  supplement  to  the  General  Electric  Review  for  May,  1910. 


ALTERNATING  CURRENT  LINES. 


8l 


distance  =  30  miles. 

distance  apart  of  wires  =  1 8  inches. 

From  these  data  we  find : 

*  • 
/  =  58.8  amperes. 

r1  =  51  ohms. 

Therefore,  from  the  table  we  find  that,  approximately,  a  No.  2 
B.  &  S.  wire  is  required  so  that   x  =  37.7  ohms. 
Furthermore, 

EI  cos  B  =  17,000  volts 

EI  sin  6  +  xl  =  12,700  volts 
and  from  equation  (i)  we  find 

r  =  37-3  ohms 

from  which  the  correct  size  of  wire  is  found  to  be,  approximately, 
a  No.  I  B.  &  S. 

36.  Calculation  of  double  line  for  two-phase  transmission  (four 
wires). — In  this  case  each  line  is  calculated  to  deliver  half  the 
prescribed  power.     Thus,  if  it  is  desired  to  deliver  1,000  kilo- 
watts at  20,000  volts  two-phase,  at  a  frequency  of  60,  line  drop 
of  3,000  volts,  etc.,  then  each  line  is  calculated  as  a  single-phase 
line  to  deliver  500  kilowatts  at  3,000  volts  line  drop. 

37.  Calculation  of  a  three-wire  transmission  line  for  three- 
phase  currents. — The  calculation  will  be  carried  out  for  the  case 
in  which  both  the  genera- 
tor and  the  receiver  are  Y- 

connected  as  shown  in  Fig. 
42.  If  it  is  desired  to  state 
the  problem  by  specifying 
the  voltage  between  mains  at 
generator  and  at  receiver, 
and  current  in  each  main,  the  specified  voltage  between  mains  may 
be  divided  by  1/3  to  give  the  values  of  E0  and  EI  in  Fig.  42. 
Let  cos  B  be  the  power  factor  of  each  receiving  circuit,  P 
the  total  power  to  be  delivered,  EI  the  electromotive  force  be- 
7 


•receiver 


|* 

i 


3 

Fig.  42. 


82 


ELECTRIC    LIGHTING. 


wire 


tween  the  terminals  of  each  receiving  circuit,  and  E0  the  elec- 
tromotive force  of  each  armature  winding  on  the  generator;  all 
prescribed  (see  Fig.  42).  Then 

P  =  3Ei I  cos  e 

from  which  the  full-load  line  current  /  may  be  calculated. 

The  numerical  difference  E0  —  EI  is  the  electromotive  force 
drop  in  one  wire.  Therefore,  looking  upon  the  problem  as  one 
in  direct  currents,  we  have  E0  —  EI  =  r'l,  where  r'  is  the  ap- 
proximate resistance  of  one  wire.  From  this  the  approximate 
size,  of  the  wire  may  be  found  from  the  table. 

Consider  one  of  the  wires,  say 
wire  number  2.  The  other  two 
wires  together  constitute  the  re- 
turn circuit  for  this  wire,  and, 
the  three  wires  being  arranged 
as  indicated  in  Fig.  43,  the  dis- 
tance from  wire  number  2  to  each 
of  the  other  wires  is  equal  to  d, 
which  is  given.  Find  the  reac- 
tance x  of  a  pair  of  wires  at 
the  prescribed  distance  apart 
center  to  center,  from  the  above 
table. 

The  component  of  E\  parallel 
to  I  is  EI  cos  9,  and  the  component  of  EI  perpendicular  to 
I  is  EI  sin  6. 

The  resistance  drop  in  one  main  is  rl  and  the  reactance  drop 
in  one  main  is  %xl,  the  former  being  parallel  to  /  and  the 
latter  being  perpendicular  to  I.  Then  the  components  of  E0 
are  EI  cos  6  +  rl,  and  EI  sin  9  +  ^xl,  respectively,  so  that 

E02  =  (Ei  cos  0  +  rl)2  +  (Ei  sin  9  + 
whence 


Fig.  43. 


l/E02  -  (Ei  sin  9  +  Y2xl)2  -  EI  cos  0 


(i) 


ALTERNATING   CURRENT   LINES.  83 

which  gives  the  true  resistance    r    of  one  wire  from  which  the 
correct  size  of  wire  is  easily  found. 

Example. — The  electromotive  force  between  mains  at  the 
receiving  station  is  to  be  20,000  volts.  Therefore,  the  electro- 
motive force  between  terminals  of  Y-connected  receiving  circuits 
would  be 

EI  =  20,000  -f-  1/3  =  1 1 ,550  volts  (see  Fig.  42) 

The  electromotive  force  between  mains  at  the  generating  sta- 
tion is  to  be  23,000  volts.  Therefore, 

Eo  =  23,000  volts  -7-  1/3  =  13,280  volts  (see  Fig.  42) 

Further  specifications:  P  =  1,000  kilowatts,  cos  6  =  0.85, 
frequency  =  60  cycles  per  second,  distance  =  30  miles,  distance 
apart  of  wires  =  21  inches. 

From  these  data  we  find  /  =  34  amperes,  and  r'  =  50.9  ohms. 
Therefore,  approximately,  a  number  5  wire  is  required.  The 
reactance  x  of  a  3O-mile  double  line  of  number  5  wires,  21  inches 
apart  center  to  center,  at  60  cycles  per  second,  is 

x  =  41.2  ohms 

which  substituted  in  equation  (i)  gives 

r  =  46.5  ohms 

so  that  a  wire  between  number  4  and  number  5  would  give  the 
prescribed  line  drop. 

38.  Line  interference. — An  alternating-current  transmission 
line  induces  an  alternating  current  in  any  adjacent  line;  this  is 
called  line  interference.  Line  interference  depends  upon  three 
distinct  effects  as  follows:  (a)  Magnetic  induction.  The  alter- 
nating-current line  acts  like  the  primary  of  an  induction  coil 
and  an  adjacent  telephone  line,  for  example,  like  the  secondary 
of  the  induction  coil,  or  in  other  words,  the  magnetic  action  of 
the  alternating  current  induces  an  alternating  electromotive  force 
in  an  adjacent  line,  (b)  Electrostatic  induction.  The  alternat- 
ing-current transmission  wires  are  repeatedly  charged  first  in  one 
sense  and  then  in  the  opposite  sense  with  the  reversals  of  the 


84  ELECTRIC   LIGHTING. 

alternating  electromotive  force,  a  repeatedly  reversed  charge  is 
produced  on  the  wires  of  an  adjacent  line  by  influence  and  the 
flow  of  this  charge  into  and  out  of  the  adjacent  line  produces  an 
alternating  current  in  the  adjacent  line,  (c)  Leakage.  If  the 
alternating-current  line  is  not  thoroughly  insulated  from  the 


Fig.  44. 

adjacent  line  more  or  less  current  leaks  across  from  one  to  the 
other. 

Line  interference  is  seldom  a  serious  matter,  except  in  the  case 
of  a  telephone  line  exposed  to  the  influence  of  an  alternating- 
current  transmission  line,  and  in  such  a  case  the  interference 
may  be  obviated  (a)  by  what  is  called  transposition  of  wires  of 
one  of  the  lines  thus  tending  to  eliminate  magnetic  and  electro- 


top  view 


tide  view 


Fig.  45. 

static  induction,  and  (b)  by  thorough  insulation,  thus  tending 
to  eliminate  leakage.* 

*  See  a  paper  by  P.  M.  Lincoln,  Transactions  of  the  American  Institute  of  Electrical 
Engineers,  Vol.  XXI,  pages  245-251,  and  a  paper  by  F.  F.  Fowle,  Transactions 
of  the  American  Institute  of  Electrical  Engineers,  Vol.  XXIII,  pages  659-689. 
The  important  part  of  this  latter  paper  is  included  in  pages  674-687. 


TRANSMISSION   LINES. 


85 


Figure  44  shows  the  essential  features  of  a  transposed  single- 
phase  (two-wire)  transmission  line.  Any  two  successive  sections 
or  loops  of  the  line  *may  be  looked  upon  as  complete  circuits 
around  which  the  current  flows  in  opposite  directions  and  across 
which  the  voltage  is  reversed  so  that  the  magnetic  actions  of 
two  successive  sections  of  the  transposed  line  on  an  adjacent 
(untransposed)  line  are  opposite  to  each  other,  and  the  electro- 
static actions  of  two  successive  sections  of  the  transposed  line 
on  an  adjacent  line  are  opposite  to  each  other. 

Line  interference  between  an  alternating  current  line  and  a 
telephone  line  may  be  eliminated  by  the  transposition  of  wires 
of  the  transmission  line  or  by  the  transposition  of  wires  of  the 
telephone  line.  It  is  more  usual  to  transpose  the  wires  of  the 


Fig.  46. 

telephone  line.  Figure  45  shows  the  method  of  transposing  a 
telephone  line.  Three  cross-arms  are  attached  to  the  pole  at 
which  the  transposition  is  to  be  made,  and  upon  the  middle  arm 
a  "two-story"  insulator  is  placed  so  as  to  bring  one  of  the  wires 
above  the  other  at  the  crossing  point  as  indicated  in  the  figure. 
Long  distance  alternating-current  transmission  lines  are  al- 
ways transposed  so  as  to  minimize  interference  with  adjacent 
lines  of  all  kinds.  Thus  Fig.  46  shows  a  cross-over  or  transposi- 
tion on  a  three-wire  three-phase  line. 


CHAPTER   IV. 

PHOTOMETRY  AND  ILLUMINATION. 

39.  Radiant  heat.     Light. — The  radiation  from  a  hot  body 
may  be  resolved  into  simple  component  parts,  each  of  which  is  a 
train  of  ether  waves  of  definite  wave-length.     All  of  these  com- 
ponent parts  of  the  total  radiation  have  one  common  property, 
namely,   they  generate  heat  in  a  body  which  absorbs  them. 
Therefore  every  portion  of  the  radiation  from  a  hot  body  is 
properly  called  radiant  heat.     The  intensity  of  a  beam  of  radiant 
heat  is  measured  by  the  heat  it  delivers  per  second  to  an  ab- 
sorbing body.     Thus,  the  radiant  heat  emitted  by  a  standard 
candle  represents  a  flow  of  about  450  ergs  of  energy  per  second 
across  one  square  centimeter  of  area  at  a  distance  of  one  meter 
from  the  candle. 

Radiant  heat  of  which  the  wave-length  lies  between  39  and  75 
millionths  of  a  centimeter  affects  the  optic  nerves  and  gives  rise 
to  sensations  of  light.  Therefore  radiant  heat  of  which  the  wave- 
length lies  between  these  limits  is  called  light.  These  limits, 
which  are  called  the  limits  of  the  visible  spectrum,  are  not 
sharply  defined,  but  vary  considerably  with  the  intensity  of  the 
radiation  and  with  the  degree  of  fatigue  of  the  optic  nerves,  and 
they  vary  greatly  with  different  persons. 

40.  The  physical  intensity  of  a  beam  of  light  is  measured  by 
its  perfectly  definite  thermal  effect,  that  is,  by  the  heat  energy  it 
delivers  per  second  to  an  absorbing  body.     Thus,  those  parts 
of  the  radiation  of  a  standard  candle  which  lie  within  the  visible 
spectrum  represent  the  flow  of  about  9.3  ergs  per  second  across 
an  area  of  one  square  centimeter  at  a  distance  of  one  meter  from 
the  candle.     Comparing  this  with  the  flow  of  energy  which  is 
represented  by  the  total  radiation  from  a  standard  candle  (450 
ergs  per  second  across  an  area  of  one  square  centimeter  at  a 

86 


PHOTOMETRY   AND    ILLUMINATION.  87 

distance  of  one  meter  from  the  candle) ,  it  follows  that  only  about 
two  per  cent,  of  the  energy  radiated  by  the  standard  candle  lies 
within  the  visible  spectrum,  that  is,  only  about  two  per  cent,  of 
the  radiation  from  the  standard  candle  is  light.  Full  sunlight 
represents  a  flow  of  about  two  million  ergs  (or  0.2  of  a  watt)  per 
second  across  one  square  centimeter.  About  one  third  or  one 
half  of  this  energy  is  absorbed  by  the  atmosphere.  The  lumi- 
nous part  of  the  sun's  rays  represents  about  four  hundred  thou- 
sand ergs  per  second,  or  0.04  of  a  watt  per  square  centimeter. 

41.  The  luminous  intensity  of  a  beam  of  light  is  presumably 
measured  by  the  intensity  of  the  light  sensation  it  can  produce, 
but  the  intensity  of  the  light  sensation  which  is  produced  by  a 
given  beam  of  light  is  extremely  indefinite.     A  given  beam  of 
light  entering  the  eye  may  produce  a  strong  or  weak  sensation, 
depending  upon  various  individual    peculiarities  of    the  person 
and  on  the  degree  of  fatigue  of  the  retina;  and  the  vividness  of 
the  sensation  depends  upon  the  extent  to  which  it  is  enhanced 
by  attention.     Our  sensations  are  not  quantitative  in  the  physical 
meaning  of  that  term;  in  fact,  they  enable  us  merely  to  dis- 
tinguish objects,  to  judge  whether  things  are  alike  or  unlike,  and 
the  certainty  and  precision  with  which  we  can  do  this  is  exempli- 
fied in  every  outward  aspect  of  our  daily  life.     The  ratio  of  the 
lumionus  intensities  of  two  beams  of  light  is  measured  by  using  a 
device  to  alter,  in  a  known  ratio,  the  physical  intensity  of  one  beam 
until  it  gives,  as  nearly  as  one  can  judge,  a  degree  of  illumination 
on  a  screen  which  is  equal  to  (like)  the  illumination  produced  by 
the  other  beam.     Such  a  device  is  called  a  photometer.  *    The 
Bunsen  photometer  is  described  in  Art.  57. 

42.  Simple  photometry  and  spectrophotometry. — The  measure- 
ment of  the  light  emitted  by  a  lamp  is  called  photometry.     This 
measurement  is  always  made  by  comparing  the  beam  of  light 

*  A  very  complete  and  interesting  discussion  of  Photometric  Devices  is  given 
by  C.  H.  Sharp,  on  pages  411-506  of  Vol.  I  of  the  Johns  Hopkins  University  Lec- 
tures on  Illuminating  Engineering,  The  Johns  Hopkins  Press,  1911, 


88  FTECTRIC  LIGHTING. 

from  a  given  lamp  with  the  beam  of  light  from  a  standard  lamp 
as  explained  in  Article  41. 

The  comparison  of  the  total  light  in  a  beam  from  a  given  lamp 
with  the  total  light  in  a  beam  from  a  standard  lamp  is  called 
simple  photometry;  whereas  the  comparison,  wave-length  by  wave- 
length, throughout  the  spectrum,  is  called  spectrophotometry  * 

The  fundamental  difficulty  in  simple  photometry  is  that  dif- 
ferent lamps  usually  show  differences  of  color,  and  these  differ- 
ences of  color  do  not  disappear  when  the  attempt  is  made  to 
adjust  a  photometer  so  that  two  lamps  give  equal  (like)  illumina- 
tion on  a  screen.  This  difficulty  is  overcome  to  some  extent 
by  the  use  of  the  flicker  photometer  which  is  described  in 
Art.  61. 

43.  Standard    lamps.     The    fundamental    light    units. — The 

British  standard  candle  is  a  sperm  candle  made  according  to  exact 
specifications.!  When  this  candle  burns  120  grains  of  sperm 
per  hour  it  is  a  standard  candle,  and  the  actual  candle-power 
during  a  given  test  is  taken  to  be  a  1 120  where  a  is  the  number 
of  grains  of  sperm  actually  burned  per  hour  during  the  test. 

The  Hefner  lamp,  {  so  called  from  its  inventor,  is  a  lamp  which 
burns  pure  amyl  acetate ;  the  wick  and  its  containing  tube  are  of 
prescribed  dimensions,  and  the  wick  is  turned  up  to  give  a  flame 
of  prescribed  height. 

The  Vernon-Har court  pentane  lamp\  is  a  lamp  which  burns  the 
vapor  of  pentane.  A  stream  of  air  flows  through  a  chamber  con- 
taining pentane,  the  air  becomes  saturated  with  pentane  vapor, 

*  Some  examples  of  the  results  of  spectrometrical  measurements  are  given  in 
Fig.  79. 

t  See  American  Gas  Light  Journal,  Vol.  LX,  page  41,  1894. 

J  A  full  discussion  of  the  Hefner  lamp  may  be  found  in  Photometrical  Measure- 
ments by  Wilbur  M.  Stine,  The  Macmillan  Co.,  1904.  In  particular,  see  the  dis- 
cussion of  Influence  of  Atmospheric  Moisture,  Influence  of  Carbon  Dioxide,  In- 
fluence of  Atmospheric  Pressure,  and  Influence  of  Atmospheric  Temperature  on 
the  brightness  of  the  Hefner  lamp  on  pages  153-157. 

§The  pentane  lamp  is  described  on  pages  132-134  of  Wilbur  M.  Stine's 
Photometrical  Measurements.  Pentane  is  one  of  the  more  volatile  constituents  of 
gasolene. 


PHOTOMETRY   AND   ILLUMINATION.  89 

and  this  mixture  of  pentane  vapor  and  air  is  burned  in  an  Argand  * 
burner  of  prescribed  dimensions. 

The  Carcel  lamp  is  2tn  Argand  burner  of  prescribed  dimensions 
burning  rape-seed  oil.  This  lamp  has  been  extensively  used  as 
a  standard  lamp  in  France. 

Light  units. — The  intensity  of  the  horizontal  beam  of  light 
from  a  Hefner  lamp  is  called  a  hefner-unit  or  a  hefner.  If  a 
lamp  were  to  give  one  hefner-unit  of  light  intensity  in  every 
direction,  the  amount  of  light,  or  the  so-called  flux  of  light  emitted 
by  the  lamp  would  be  what  is  called  one  spherical-hefner. 

The  candle,  or  candle-unit,  or  candle-power,  as  it  is  variously 
called,  is  a  beam  of  light  of  which  the  intensity  is  i.n  hefner- 
units ;  that  is  to  say,  a  horizontal  beam  from  a  Hefner  lamp  has  an 
intensity  of  0.90  candle-power.  This  is  the  definition  of  the 
candle-power  which  is  used  by  the  United  States  Bureau  of 
Standards,  and  the  candle-power  so  defined  is  called  the  inter- 
national candle  to  distinguish  it  from  the  old  British  Standard 
Candle  which  is  now  obsolete. 

A  lamp  which  would  give  one  candle-unit  of  intensity  in  every 
direction  would  emit  one  spherical-candle  of  light  flux. 

For  most  photometric  work  nothing  is  better  as  a  working 
standard  than  a  properly  aged  and  standardized  incandescent  lamp. 
Such  lamps  can  be  obtained  from  the  United  States  Bureau  of 
Standards  with  certificates  specifying  their  candle-power  in  a 
prescribed  direction  when  operated  with  a  prescribed  voltage 
between  their  terminals. 

44.  Conical  intensity  and  sectional  intensity  of  a  beam  of  light. 

— The  expression,  intensity  of  a  beam  of  light,  which  is  used  in  the 
above  definitions  of  the  hefner-unit  and  candle-unit,  refers  to  the 
amount  of  light  in  a  unit-sized  cone  of  rays.  This  conical 
intensity,  which  it  may  be  called  for  brevity,  is  expressed  in 

*  The  Argand  burner  is  a  type  of  burner  in  which  a  supply  of  air  is  admitted 
to  the  interior  of  a  flame,  as  in[the  familiar  student  lamp.  See  article  Argand  burner 
in  any  good  encyclopaedia. 


90  ELECTRIC   LIGHTING. 

Hefners  or  candles;  and  it  is  independent  of  distance,  since  the 
light  in  a  given  cone  of  rays  always  remains  in  that  cone.* 

The  intensity  of  a  beam  of  light  may  also  refer  to  the  amount 
of  light  per  unit  sectional  area  of  the  beam.  This  sectional  inten- 
sity, which  it  may  be  called  for  brevity,  decreases  as  the  square 
of  the  distance  from  the  lamp  increases,  as  explained  in  Art.  48. 

45.  Intrinsic  brilliancy  of  a  lamp. — The  candle-power  of  a 
lamp  in  a  given  direction  divided  by  the  luminous  area  f  of  the 
lamp  is  called  the  intrinsic  brilliancy  of  the  lamp. 

Examples. — The  intrinsic  brilliancy  of  the  crater  of  a  powerful 
carbon-arc  lamp  approaches  two  hundred  thousand  candles  per 
square  inch.  The  tungsten-filament  lamp  has  an  intrinsic  bril- 
liancy of  about  one  thousand  candles  per  square  inch.  The 
carbon-filament  lamp  has  an  intrinsic  brilliancy  of  about  three 
hundred  candles  per  square  inch.  A  kerosene  lamp  flame  has 
an  intrinsic  brilliancy  of  from  four  to  eight  candles  per  square 
inch. 

A  lamp  of  great  intrinsic  brilliancy  is  very  painful  to  look  at, 
and  such  a  lamp  should  always  be  surrounded  by  a  diffusing 
globe  or  shade  so  as  to  hide  the  luminous  surface  of  the  lamp 
itself.  Thus,  an  arc  lamp  when  used  indoors  is  always  provided 
with  a  diffusing  globe,  and  the  tungsten  lamp  should  always  have 
a  diffusing  globe  or  shade  when  it  is  used  for  interior  lighting. 

46.  Unit  of  spherical  angle.     Definition  of  the  lumen. — To 

understand  the  relationship  of  the  various  light  units  one  must 
understand  what  is  called  solid  or  spherical  angle.  Consider  a 
cone  and  a  sphere  with  its  center  at  the  apex  of  the  cone.  Let 
A  be  the  area  of  the  spherical  surface  which  is  inside  the  cone, 

*  It  is  assumed  in  these  fundamental  definitions  that  the  light  source  is  very 
small  in  size;  it  requires  a  very  elaborate  discussion  to  establish  the  fundamental 
ideas  of  photometry  if  this  assumption  is  not  made. 

Some  matters  relating  to  light  sources  which  are  not  negligibly  small  are  dis- 
cussed in  Arts.  50  and  56.  A  good  example  of  the  application  of  the  fundamental 
ideas  of  photometry  to  large  luminous  sources  is  the  paper,  "Geometrical  Theory 
of  Radiating  Surfaces  with  Discussion  of  Light  Tubes,"  by  E.  P.  Hyde,  Bulletin 
of  the  Bureau  of  Standards,  Vol.  Ill,  pages  81-104,  1907. 

t  Projected  area  at  right  angles  to  the  given  direction. 


PHOTOMETRY   AND    ILLUMINATION.  91 

and  let  r  be  the  radius  of  the  sphere.  Then  the  ratio  A/r2 
measures  what  is  called  the  spherical  angle  of  the  cone.*  Thus 
one  unit  of  spherical  angle  is  subtended  by  one  square  meter 
of  the  surface  of  a  sphere  of  one  meter  radius,  or  by  one  square 
foot  of  a  sphere  of  one  foot  radius  and  the  complete  surface  of  a 
sphere  represents  \-w  units  of  spherical  angle.  In  the  following 
discussion  one  unit  of  spherical  angle  is  called  a  unit-cone. 

Imagine  a  lamp  which  gives  an  intensity  of  one  candle-power 
in  every  direction.  The  amount  of  light,  or  light  flux,  passing 
out  from  such  a  lamp  in  one  unit-cone  is  called  the  lumen  of  light 
flux.  Such  a  lamp  would  emit  one  spherical-candle  of  light  flux, 
inasmuch  as  the  conical  intensity  is  assumed  to  be  one  candle- 
power  in  every  direction;  but  the  whole  spherical  surface  repre- 
sents 4?r  unit-cones,  each  of  which  contains  one  lumen  of  light; 
therefore  there  are  4?r  lumens  of  light  flux  in  one  spherical-candle. 

47.  Sectional  intensity  of  a  beam  of  light.  Definition  of  the 
foot-candle.  Definition  of  the  lux. — Imagine  a  lamp  which  gives 
out  one  candle-power  in  every  direction,  and  consider  a  sphere 
of  one  foot  radius  with  its  center  at  the  lamp.  One  square  foot 
of  the  surface  of  this  sphere  is  contained  inside  of  a  unit-cone,  and 
such  a  unit-cone  contains  one  lumen  of  light  flux.  Therefore 
one  lumen  of  light  flux  passes  through  each  square  foot  of  the 
surface  of  the  sphere;  that  is,  the  light  which  radiates  from  the 
given  lamp  has  a  sectional  intensity  of  one  lumen  per  square 
foot  at  a,  distance  of  one  foot  from  the  lamp.  This  sectional 
intensity  is  sometimes  called  the  foot-candle.  That  is  to  say, 
the  foot-candle  is  the  sectional  intensity  of  a  one-candle-power 
beam  at  a  distance  of  one  foot  from  the  lamp. 

The  meter-candle  is  the  sectional  intensity  of  a  one-candle- 
power  beam  at  a  distance  of  one  meter  from  the  lamp.  The 
meter-candle  is  one  lumen  per  square  meter  and  it  is  sometimes 
called  the  lux. 

*  To  express  the  value  of  a  spherical  angle  as  the  quotient  of  the  spherical  area 
divided  by  square  of  spherical  radius  is  analogous  to  the  method  of  expressing  a 
plane  angle  as  the  quotient  of  the  arc  of  a  circle  divided  by  the  radius. 


92  ELECTRIC   LIGHTING. 

One  foot-candle  is  equal  to  10.75  meter-candles  or  luxes. 
The  relation  between  the  various  light  units  may  be  kept  in 
mind  most  easily  with  the  help  of  Fig.  47. 

sphere 
one  foot  radius 


one  lumen 
of  light 


Fig.  47. 

48.  The  law  of  inverse  squares. — It  is  evident  that  the  sec- 
tional intensity  of  a  beam  of  light  from  a  lamp  decreases  with 
increasing  distance  from  the  lamp.  Indeed  the  sectional  in- 
tensity of  a  beam  from  a  lamp  is  given  by  the  equation 


(14) 


in  which  C  is  the  conical  intensity  of  the  beam  in  candle-power, 
and  I  is  the  sectional  intensity  of  the  beam  in  foot-candles  at 
a  distance  of  d  feet  from  the  lamp.  This  is  evident  when  we 
consider  that  the  amount  of  light  in  a  cone  of  rays  remains 
constant,  whereas  the  sectional  area  of  the  cone  increases  as 
the  square  of  the  distance  from  the  apex  of  the  cone. 

Equation  (14)  expresses  what  is  called  the  laiv  of  inverse  squares. 
This  law  applies  strictly  to  the  light  which  comes  from  a  very 


PHOTOMETRY   AND    ILLUMINATION. 


93 


small  portion  of  the  luminous  surface  of  a  lamp,  a  point  source 
as  it  is  called.  The  law  is  approximately  true,  however,  for 
a  whole  lamp  at  distances  which  are  large  compared  with  the 
size  of  the  luminous  surface  of  the  lamp.  For  example,  con- 
sider the  light  which  is  given  off  by  a  brightly  illuminated  flat 
disk  of  paper.  The  sectional  intensities  of  this  light  at  points  on 
the  axis  of  the  disk  at  different  distances  from  the  disk  are  ex- 
hibited in  the  accompanying  table.  The  heavy-faced  num- 
bers show  what  the  sectional  intensities  would  be  according 
to  the  law  of  inverse  squares,  and  the  light-faced  figures  show 
the  actual  intensities. 

PAPER   DISK   2   FEET    IN    DIAMETER. 


Distances  from  Disk  in  Feet. 

5 

10 

20 

40 

80 

160 

Sectional    intensities   according    to 
the  law  of  inverse  squares     
Actual  sectional  intensities  

1024 

984.6 

256 

253.5 

64 

63.84 

16 

15-99 

3.9992 

I 
0.99996 

The  error  of  the  law  of  inverse  squares  does  not  exceed  two- 
tenths  of  one  per  cent,  for  distances  exceeding  ten  times  the  maxi- 
mum dimension  of  the  luminous  surface  of  the  lamp.  See  Art.  50. 

49.  To  find  the  relation  between  the  intrinsic  brilliancy  and  the  lumens  of 
light  emitted  per  square  foot  of  a  flat  diffusing  surface  of  plaster  or  uncalendered 
paper. — Consider  a  small  element  AA  of  the  plaster  surface,  and  let  Cn  be  the 
candle-power  of  the  beam  which  is  given  off  by  the  element  normally.  Then 
C»/AA(  =  B)  is  the  intrinsic  brilliancy  of  the  plaster  surface  according  to  Art.  45. 
The  candle  power  of  the  normal  beam  is  therefore  Cn  =  B  •  AA  and  the  candle- 
power  of  the  oblique  beam  b,  Fig.  48,  is  equal  to  Cn  cos  6  according  to  Lambert's 
cosine  law  (see  Art.  53).  Therefore  we  have: 

Cb  =  B  cos  0  .  AA  (i) 

in  which  Cb  is  the  candle-power  of  the  oblique  beam  6  in  Fig.  48,  B  is  the  in- 
trinsic brilliancy  of  the  plaster  surface,  AA  is  the  area  of  the  plaster  surface,  and 
0  is  the  angle  shown  in  the  figure. 

Consider  the  zone  zz  of  the  reference  sphere,  the  zone  extending  entirely 
around  the  "pole"  p.  The  area  of  this  zone  is  nrr  sin  0  X  r  •  A0,  the  sectional 
intensity  of  the  beam  b  at  zz  is  equal  to  C&/r2  according  to  equation  (14),  and  the 
amount  of  light  passing  through  the  zone  zz  is  equal  to  the  product  of  the  area  of 
zz  and  the  sectional  intensity  of  b.  Therefore  we  have 


94 


ELECTRIC   LIGHTING. 


sin  0  cos  0  •  A0 


in  which    AL    is  the  amount  of  light  in  lumens  passing  through    22. 

To  find  the  total  amount  of  light 
L  emitted  by  the  element  of  plaster 
surface,  equation  (ii)  must  be  inte- 
grated between  the  limits  0  =  o  to 
0  =  90°,  which  gives: 


sphere  of 
radius  r 


whence 


B  = 


•  AA 
L 


(iii) 


(iv) 


That  is,  the  intrinsic  brilliancy  of  a 
flat  diffusing  surface  of  plaster  or  un- 
calendered  paper  is  equal  to  the  lu- 
mens of  light  emitted  per  unit  area 
(L/AA)  divided  by  TT. 

50.  Given  a  flat  circular  disk  of 
plaster  or  uncalendered  paper  of 
which  the  intrinsic  brilliancy  is  B, 
to  find  the  amount  of  light  falling  on 
unit  area  at  a  point  p  in  the  axis  of 
the  disk  as  shown  in  Fig.  49. — Con- 
sider the  beam  of  light  which  reaches 
p  from  a  small  element  e  of  the  cir- 
cular strip  55  of  the  plaster  disk  DD. 
The  conical  intensity  of  this  beam  is 
given  by  equation  (i),  where  AA  is  the 

area  of  the  element  e;  and  the  sectional  intensity  of  the  beam  at  p  is  found  by  di- 
viding Cb  by  the  square  of  the  distance  ep  which  is  (JR2  +  P2)-  Therefore,  multi- 
plying this  sectional  intensity  by  the  projected  value  of  the  unit  of  area  at  p 
(namely  unit  of  area  X  cos  0),  we  find  the  amount  of  light  falling  upon  the  unit 
of  area  at  p  from  the  element  e.  But  every  element  of  the  circular  strip  55  sends 
the  same  amount  of  light  to  the  unit  of  area  at  p,  and  therefore  the  total  amount 
of  light  AL  received  by  the  unit  of  area  at  p  from  the  entire  circular  strip  55  is 


Fig.  48. 


AL  =  B  X  2trp .  Ap  X 


R* 


X  cos*  B 


but 


cos  0  '=  •   ,        — ~» 


so  that  equation  (v)  becomes: 


=  2irBR* 


p.Ap 


(v) 


(iv) 


and  the  total  amount  of  light  falling  on  unit  of  area  at  p  from  the  entire  disk  DD 
is  found  by  integrating  equation  (vi),  from  p  =  o    to    p  —  r,    that  is, 


PHOTOMETRY   AND    ILLUMINATION. 


95 


2TTBR2 


or 


c* 

irBr* 


p.dp 


R* 


(vii) 
(viii) 


And  of  course  the  lumens  of  light  received  by  the  unit  of  area  at  p,  in  Fig.  49, 
is  the  intensity  of  illumination  of  the  unit  of  area  by  the  light  from  the  plaster  or 
paper  disk.  The  actual  sectional  intensities  which  are  given  in  the  table  in  Art. 
48  were  calculated  from  equation  (viii) ,  using  r  =  one  foot,  and  using  for  R  the 
series  of  values  5  feet,  10  feet,  20  feet,  40  feet,  etc. 


front  view 


side  view 


51.  The  intensity  of  illumination  of  a  surface  depends  upon 
the  amount  of  light  falling  upon  one  unit  of  area  of  the  surface. 
Therefore,   intensity  of  illumination  is  expressed  in  terms  of 
the  same  unit  as  sectional  intensity  of  a  beam  of  light.     Thus 
an  intensity  of  illumination  of  one  lux,  or  one  meter-candle, 
is  one  lumen  of    light    falling  an  each  square  meter;   it  is  the 
intensity  of  illumination  produced  by  a  standard  candle  at  a 
distance  of  one  meter.     The  foot-candle  is  the  intensity  of  illu- 
mination at  a  distance  of  one  foot  from  a  standard  candle; 
it  is  equal  to  one  lumen  per  square  foot. 

Examples. — The  light  from  a  lo-candle-power  lamp  falls 
perpendicularly  upon  a  sheet  of  paper  at  a  distance  of  two  feet 
from  the  lamp.  Substituting  C  =  10  and  d  =  2,  in  equation 
(14)  we  find  the  value  of  7  to  be  2.5  foot-candles. 

52.  Oblique  illumination  of  a  flat  surface. — When  a  beam  of 
light  falls  obliquely  upon  a  flat  surface  as  shown  in  Fig.  50,  the 


96 


ELECTRIC   LIGHTING. 


light  is  spread  over  an  area  greater  than  the  sectional  area  of 
the  beam  in  the  ratio  acjab,  and  therefore  the  intensity  of  illu- 
mination of  the  surface  is  less  than  the  sectional  intensity  of 

the  beam  in  the  ratio  ab/ac. 
That  is  to  say,  the  intensity 
of  illumination  of  the  surface 
is  equal  to  /  cos  6  where  / 
is  the  sectional  intensity  of  the 
beam  and  6  is  the  angle  shown 
in  Fig.  50. 

Let  C  be  the  conical  inten- 
sity of  the  beam   bb  from  a 
lamp  as   shown  in   Fig.   51, 
and  let  us  consider  the  inten- 
sity of  illumination  In   on  a 

surface  normal  to  the  beam  at  p,  the  intensity  of  illumi- 
nation JA  on  a  horizontal  surface  at  p,  and  the  intensity  of 
illumination  Iv  on  a  vertical  surface  at  p.  The  sectional  in- 
tensity of  the  beam  at  p  is  C/d?  according  to  equation  (14), 


Fig.  50. 


Fig.  51. 

and,  since  the  normal  intensity  of  illumination  produced  by 
a  beam  is  equal  to  the  sectional  intensity  of  the  beam,  therefore 
we  have 

C 


In       d? 


(15*) 


PHOTOMETRY  AND   ILLUMINATION  97 

Furthermore  from   the  above  discussion  of  Fig.   50  we  have 

(i6a) 


C 

=  -^  •  cos 


Iv  =  -    •  sin  0 


(I7a) 


where    6   is  the  angle  shown  in  Figs.  50  and  51. 

In  many  cases  the  height  H  of  the  lamp  above  the  illuminated 
plane  qp  and  the  angle  6  are  given  to  find  /„,  IH  and  Iv. 
In  such  cases  more  convenient  equations  can  be  obtained  by 
substituting  d  =  H/cos  0  in  the  above  equations  giving 


cos^ 


and 


C 
-^>  •  cos3  0 


c 
Iv  =  -=p,  •  sin  0  cos2 


(166) 
(176) 


from  lamp 


53.  Regular  reflection  and  diffuse  reflection.  Lambert's 
cosine  law. — The  reflection  from  a  polished  surface  like  a  mirror 
is  called  regular  reflection.  The 
reflection  from  a  rough  surface 
like  plaster  or  uncalendered  paper, 
is  called  diffuse  reflection. 

Most  surfaces  show  both  regular 
reflection  and  diffuse  reflection. 
Thus  everyone  is  familiar  with  the 
unpleasant  shining  reflection  from  the  page  of  a  book  when  it 
is  viewed  as  shown  in  Fig.  52.  A  scraped  plaster  surface  has 
no  perceptible  regular  reflection.  The  following  statements  refer 
to  such  a  surface. 

Proposition    (a). — The  apparent   brightness  of  an  illuminated 
plaster  surface  is  independent  of  its  distance  from  the  observer's 
8 


page  of  book 

Fig.  52. 


98  ELECTRIC    LIGHTING. 

eye.  This  may  be  understood  from  the  following  argument. 
If  the  distance  of  the  illuminated  surface  from  the  eye  is  doubled 
then,  according  to  the  law  of  inverse  squares,*  one  quarter  as 
much  light  enters  the  eye  from  the  surface  (size  of  pupil  remain- 


„  -  -  ~*i  normal  to 

plaster  surface 


one  square  foot  of/ 
^plaster  surface] 

Fig.  53. 

ing  unchanged),  but  the  image  of  the  illuminated  sufrace  on 
the  retina  is  reduced  to  one  quarter  of  its  original  area,  so 
that  one  quarter  as  much  light  falls  on  one  quarter  as  large  a 
spot  on  the  retina,  and  therefore  the  intensity  of  illumination  of 
the  retina  is  unchanged. 

Proposition  (6). — Surfaces  like  rough  plaster  and  uncalendered 
paper,  which  diffuse  light  very  completely,  have  an  apparent  bright- 
ness which  remains  the  same  as  they  are  viewed  more  and  more 
obliquely.  This  is  an  observed  fact,  and  an  important  conse- 
quence of  it  is  as  follows.  Consider  one  square  foot  of  an  illumi- 
nated plaster  surface  which  is  viewed  obliquely  as  shown  in 
Fig-  53>  so  that  the  projected  area  pp  of  the  plaster  surface  is  re- 
duced, say,  to  one  half  of  a  square  foot.  Then  the  area  of  the 
image  on  the  retina  is  one  half  as  great  as  it  would  be  if  the 
plaster  surface  were  turned  at  right  angles  to  the  line  of  vision 
(the  distance  of  the  eye  from  plaster  surface  remaining  un- 
changed). But  to  make  the  plaster  surface  appear  of  the  same 
brightness  in  Fig.  53  with  the  image  on  the  retina  reduced  to 
half-size  (in  area),  one  half  as  much  light  must  enter  the  eye. 

*  The  law  of  inverse  squares  is  true  for  a  small  portion  of  an  illuminated  surface. 


PHOTOMETRY   AND    ILLUMINATION.  99 

That  is  to  say,  when  an  illuminated  diffusing  surface  is  viewed 
obliquely  so  that  the  apparent  area  of  the  surface  is  reduced  say 
to  one  half,  then  tha  amount  of  light  which  enters  the  eye  from 
the  surface  is  reduced  to  one  half  also.  In  general  the  apparent 
area  of  a  flat  surface  is  reduced  in  the  ratio  I  :  cos  0,  where  0 
is  the  angle  shown  in  Fig.  53.  Therefore  the  intensity*  of  the 
light  given  off  in  the  direction  ab,  Fig.  53,  is  less  than  the 
intensity*  of  the  light  given  off  in  the  direction  cd  in  the  ratio 
I  :  cos  6.  This  relation  is  called  Lambert's  cosine  law. 

Consider  the  light  emitted  by  an  element  A^4  of  an  illuminated 
surface,  the  element  being  so  small  that  it  may  be  considered  as 
a  point  source  of  light.  Then  the  I 

j 

candle  power  of  the  light  beam 
emitted  normally  to  the  element     \ 

is  B  •  AA ,  where  B  is  the  intrinsic      0 \  j  v 

1    M«.  r    1  r  \         Q     y  normal  to 

brilliancy  of  the  surface,  and  the  Xt'""  *"v  Poster  surface 

candle  power  of  the  beam   bb,   in 


Fig.  54,  is  j5-cos  6-kA. 

54.  Absorption  of    light  by  il- 
luminated   surfaces.  —  An    abso- 
lutely white  surface  would  be  a 
surface  which  would  reflect    (dif- 
fusely) all  of  the  light  falling  upon  Fig  54 
it.     Consider  a  surface  which  re- 
flects, say,  0.6  of  the  light  which  falls  upon  it  and  which  absorbs 
the  remaining  0.4  of  the  light.     The  fraction  0.6  is  called  the  re- 
flection coefficient  of  the  surface,  and  the  fraction  0.4  is  called 
the  absorption  coefficient  of  the  surface.     The  reflection  coeffi- 
cient of  a  rough  surface  is  sometimes   called  the  albedo  of  the 
surface. 

55.  Change  of  conical  intensity  by  lenses.     When  the  light 
source  is  very  small. — Light  from  a  small  source     A     passes 
through  a  lens  and  is  brought  to  a  focus  at   B,    as  shown  in  Fig. 

*  Conical  intensity;  or  sectional  intensity  at  a  given  distance  from  the  plaster 
surface;  see  following  paragraph. 


100 


ELECTRIC    LIGHTING. 


COEFFICIENTS  OF   REFLECTION*  OF  WALL   PAPERS. 


Material. 

Coefficients  of  Re- 
flection. 

Coefficients  of  Ab- 
sorption. 

White  blotting  paper 

o  82 

o  18 

^Vhite  cartridge  paper    . 

o  80 

Ordinary  foolscap  paper  

0.70 

o  10 

Chrome  yellow  paper 

o  62 

o  38 

Orange  paper  

O  ^O 

o  50 

Yellow  wall  paper  . 

O.4O 

o  60 

Yellow  painted  wall 

O.4O 

o  60 

Light  pink  paper 

o.^?6 

o  64 

Yellow  cardboard 

o.^o 

o  70 

Light  blue  cardboard  

0.25 

0.75 

Brown  cardboard  

O.2O 

0.80 

Yellow  painted  wall  (dirty)  
Emerald  green  paper.  

O.2O 

0.18 

0.80 
0.82 

Dark  brown  paper  

0.13 

0.87 

Vermilion  paper  
Bluish  green  paper  
Cobalt  blue  paper  

0.12 
0.12 
O.I  2 

0.88 
0.88 
0.88 

Black  paper  

O.OS 

0.95 

Ultamarine  blue  paper  
Black  velvet  

0-035 
O.OO4 

0.965 
0.996 

55.  Beyond  the  focus  B  the  light  spreads  out  again  in  a  conical 
beam  gg  as  shown  in  the  figure.  It  is  evident  that  the  conical 
intensity  of  the  beam  gg  is  the  same  as  the  conical  intensity  of 


lens 


Fig.  55. 

the  beam  ff  because  the  total  amount  of  light  is  the  same  in 
both  beams  and  both  cones  are  of  the  same  size.  Let  C  be  the 
conical  intensity  of  the  beam  ee,  and  C'  the  conical  intensity 
of  the  beam  ff  (or  of  the  beam  gg).  Then 


*  Taken  from  the  Standard  Handbook  for  Electrical  Engineers,  section  12,  para- 
graph 37,  by  Louis  Bell. 


PHOTOMETRY   AND    ILLUMINATION. 


101 


C" 


(18) 


in  which  a  and  b  are  the  distances  indicated  in  the  figure.  This 
equation  is  based  on  the  assumption  that  no  light  is  lost  in 
passing  through  the  lens.  Let  S  be  the  area  of  the  lens.  Imag- 
ine a  sphere  of  radius  a  with  its  center  at  A,  and  a  sphere  of 
radius  b  with  its  center  at  B.  The  portions  of  these  spherical 
surfaces  which  are  included  within  the  cones  ee  and  ff  are 
approximately  equal  in  area  to  S.  Therefore  the  spherical  angle 
of  the  cone  ee  is  equal  to  5/a2  and  the  spherical  angle  of  the 
cone  ff  is  equal  to  S/62.  Let  L  be  the  amount  of  light-flux 
in  the  cone  ee,  then  the  conical  intensity  of  the  beam  ee  is 
equal  to  L  divided  by  S/a2,  and  the  conical  intensity  of  the 
beam  //  is  equal  to  L  divided  by  S/b2.  That  is,  C  =  La?/S 
and  C'  =  Lb2/S,  whence  equation  (18)  follows  at  once. 

' 


K • 


Fig.  56. 


The  action  of  a  concave  mirror  is  the  same  as  the  action  of  a 
converging  lens  in  altering  the  conical  intensity  of  a  beam  of 
light. 

The  above  discussion  applies  also  to  Fig.  56  in  which  the  light 
source  A  is  inside  of  the  principal  focus  F. 

If  the  distance  a  in  Fig.  55  is  equal  to  the  focal  length  of  the 
lens,  then  the  emergent  beam  ff  is  a.  beam  of  parallel  rays,  or, 
in  other  words,  the  distance  b  is  infinity.  Thus,  Fig.  57  shows 
a  very  small  light  source  placed  at  the  principal  focus  of  a  con- 
verging lens.  In  this  ideal  case  (ideal  in  that  the  source  is  as- 


IO2 


ELECTRIC   LIGHTING. 


sumed  to  be  a  point)  the  beam  ff  is  a  beam  of  parallel  rays,  and 
the  conical  intensity  of  the  beam  ff  is  infinitely  greater  than  the 
conical  intensity  of  the  beam  ee,  according  to  equation  (18). 


lens 


b  (=  infinity) 


1  focal  length* 
of  lens 


Fig.  57. 


But  there  is  no  such  thing  physically  as  a  point  source,  and  when 
an  actual  light  source  is  placed  at  the  principal  focus  of  a  lens 
or  concave  mirror,  the  size  of  the  light  source  must  be  taken  into 
consideration  in  the  discussion  of  the  action  of  the  lens  or  mirror, 
as  in  the  following  article. 

56.  The  searchlight. — The  searchlight  consists  of  a  lamp  placed 
at  the  principal  focus  of  a  lens  or  concave  mirror.     The  action 


tens 


*--*--< 


side  view 


front  view  of  screen 


Fig.  58. 


of  the  searchlight  is  shown  in  Fig.  58,  in  which  the  luminous  source 
is  a  gas  flame.  The  light  from  each  point  p  of  the  flame  is  con- 
verted into  a  beam  of  parallel  rays  by  the  lens  as  shown  in  the  figure. 
Therefore  the  light  from  each  point  of  the  source  illuminates  a 


PHOTOMETRY   AND    ILLUMINATION. 


103 


circular  spot  ss  on  a  distant  screen,  and  the  diameter  of  this 
spot  is  equal  to  the  diameter  of  the  lens.  The  illuminated  field 
on  the  distant  scree  A  consists  of  a  central  portion  UU  which  is 
uniformly  illuminated  (if  the  flame  is  uniformly  bright),  and  a 
fringe  PP  which  shades  off  gradually  to  complete  darkness  as 
shown  in  the  figure.  In  fact  the  illuminated  field  produced 
by  a  searchlight  is  an  inverted  blurred  image  of  the  source,  as 
may  be  understood  by  a  careful  study  of  Fig.  58.  Thus,  one 
sees  a  large  inverted  blurred  image  of  the  acetylene  flame  of  an 
automobile  searchlight  when  the  searchlight  beam  falls  on  a  flat 
surface  like  the  side  of  a  house. 

When  the  light  source  is  uniformly  bright,  then  the  beam  from  a 
searchlight  has  a  definite  conical  intensity  at  a  great  distance 
from  the  lamp,  as  may  be  understood  from  the  following  con- 
siderations. If  the  screen  in  Fig.  58  is  at  a  very  great  distance 
from  a  searchlight,  the  diameter  of  55  becomes  negligible  in 
comparison  with  the  di- 
ameter of  the  illuminated 
field,  or,  in  other  words, 
the  fringe  of  the  illumi- 
nated field  becomes  neg- 
ligible. That  is  to  say, 
all  of  the  light  in  the 
searchlight  beam  may  be 
thought  of  as  being  con- 
tained within  the  cone 
rr,  and  consequently  the 
searchlight  beam  may  be 
thought  of  as  having  a 
definite  conical  intensity. 

To  determine  the  conical  intensity  of  the  beam  of  a  searchlight, 
consider  a  source  AA,  Fig.  59,  placed  at  the  principal  focus  of  a 
lens  as  shown.  The  light  which  falls  upon  the  lens  is  contained 
within  the  cone  ee,  and  the  searchlight  beam  at  a  great  distance 
from  the  lens  is  contained  in  the  cone  rr  as  above  explained. 


Fig.  59. 


104  ELECTRIC    LIGHTING. 

Therefore,  assuming  that  no  light  is  lost  in  the  lens,  the  conical 
intensity  of  the  searchlight  beam  is  greater  than  the  conical 
intensity  of  the  beam  from  the  lamp  in  the  inverse  ratio  of  the 
spherical  angles  of  the  two  cones  ee  and  rr  in  Fig.  59.  Let  s 
be  the  area  of  the  luminous  surface  of  the  lamp  AA  in  Fig.  59, 
and  let  5  be  the  area  of  the  lens.  Then  the  spherical  angle  of 
the  cone  rr  is  sensibly  equal  to  s/f,  and  the  spherical  angle  of 
the  cone  ee  is  sensibly  equal  to  5//2.  Multiplying  the  conical 
intensity  of  the  beam  ee  by  the  spherical  angle  of  the  cone  ee 
gives  the  number  of  lumens  of  light  that  strike  the  lens.  Ignoring 
loss  of  light,  this  is  the  amount  of  light  in  the  cone  rr,  and  it 
may  be  divided  by  the  spherical  angle  of  the  cone  rr  to  give  the 
conical  intensity  of  the  searchlight  beam. 

In  the  above  discussion  the  lens  or  mirror  is  supposed  to  be 
entirely  free  from  the  error  called  spherical  aberration.  This  is 
never  the  case  in  practice,  especially  with  a  lens  or  mirror  whose 
diameter  is  large  as  compared  with  its  focal  length.  The  effect 
of  spherical  aberration  is  to  cause  more  blurring  on  a  distant 
screen  than  is  represented  in  Fig.  58  and  to  cause  a  slightly  in- 
creased divergence  of  the  searchlight  beam. 

As  before  stated,  it  is  proper  to  speak  of  the  candle-power 
(conical  intensity)  of  a  searchlight  beam  when  the  lamp  presents 
a  uniformly  brilliant  surface  and  when  the  searchlight  beam  is 
considered  only  at  great  distances  from  the  search  lamp.  The 
effect  of  spherical  aberration  is  to  make  it  more  generally  per- 
missible to  speak  of  the  candle-power  of  a  searchlight  beam, 
because  the  blurring  due  to  spherical  aberration  tends  to  make 
the  central  portion  of  the  field  in  Fig.  58  uniformly  illuminated 
even  when  the  lamp  does  not  present  a  uniformly  illuminated 
surface.  This  is  especially  the  case  in  a  searchlight  using  a  closely 
coiled  tungsten-filament  lamp.  The  illuminated  field  on  a  dis- 
tant screen  is  of  course  a  blurred  image  of  the  filament,  and  it 
is  not  permissible  to  speak  of  the  candle-power  of  the  searchlight 
beam  unless  the  blurring  is  sufficient  to  obliterate  every  trace 
of  this  image  of  the  filament. 


PHOTOMETRY   AND    ILLUMINATION. 


105 


When  a  lamp  having  a  small  straight  filament  is  used  in  a 
searchlight,  then  to  confine  the  searchlight  beam  to  the  smallest 
possible  cone,  it  is  best  to  arrange  the  filament  in  the  axis  of  the 
lens  or  mirror  as  shown  in  Fig.  60.  Thus  the  light  from  the 


lens 


b  'focal 
,  plane 


Fig.  60a. 


Fig.  60&. 


small  straight  filament  cd,  in  Fig.  60,  may  be  thought  of  as 
coming  from  a  circular  spot  ab  on  the  focal  plane,  and  ab  is 
much  shorter  than  cd,  if  the  focal  length  of  the  lens  is  large  as 
compared  with  its  diameter. 

When  the  diameter  of  the  lens  or  mirror  is  large  as  compared 
with  its  focal  length,  as  shown  in  Fig.  61,  then  the  only  feasible 


Fig.  6ia 


Fig.  61&. 


method  of  finding  the  best  position  of  the  lamp  filament  is  by 
trial ;  it  is  not  feasible  to  calculate  the  relative  advantages  of  the 
two  positions  shown  in  Fig.  6ia  and  Fig.  6ib. 

57.  The  Bunsen  photometer. — The  most  extensively  used 
device  for  comparing  the  conical  intensities  of  the  light  from  two 
lamps  is  the  Bunsen  photometer.  A  given  lamp  and  a  standard 
lamp  are  placed  at  the  ends  of  a  horizontal  bar,  and  a  screen 
(see  Fig.  62)  of  thin  paper  is  moved  along  the  bar  until  the  two 


io6 


ELECTRIC   LIGHTING. 


sides  of  the  screen  are  equally  illuminated  by  the  two  lamps. 
Equal  intensities  of  illumination  on  the  two  sides  of  the  screen 
indicate  equal  sectional  intensities  (at  the  screen)  of  the  beams 
from  the  two  lamps.  Let  C  and  C'  be  the  conical  intensities  of 
the  beams  from  the  two  lamps  as  shown  in  Fig.  62.  Then  the 


standard 
lamp 


screen 


given 
lamp 


JL. 


Fig.  62. 


sectional  intensity  at  the  screen  of  the  beam  from  the  standard 
lamp  is  C/d2,  and  the  sectional  intensity  at  the  screen  of  the 
beam  from  the  given  lamp  is  C'/d  ,  according  to  equation  (14), 
and  since  these  sectional  intensities  are  equal,  as  above  explained, 
we  have 

C      C 


7/2 


or 


C 
C' 


(19) 


from  which  the  ratio  of  the  conical  intensities  may  be  calculated 
when   d  and   df   have  been  observed. 

An  irregular  grease  spot  on  the  thin  paper  screen  enables  one 
to  judge  better  when  the  illumination  is  the  same  on  the  two 
sides  of  the  screen.  This  spot  should  be  made  with  clean  paraf- 
fine,  and  the  excess  of  paraffine  should  be  drawn  out  of  the  screen 
by  placing  it  between  folds  of  absorbent  paper  and  applying  a 
hot  flat-iron.  To  facilitate  the  seeing  of  both  faces  of  the  screen 
simultaneously  two  mirrors  are  usually  placed  as  shown  in  Fig. 

63- 

In  judging  the  equality  of  illumination  on  the  two  sides  of  the 


PHOTOMETRY   AND    ILLUMINATION. 


107 


Bunsen  photometer  screen,  one  eye  only  should  be  used.  In 
using  both  eyes,  one  unconsciously  looks  at  one  side  of  the  screen 
with  one  eye  and  aUthe  other  side  of  the  screen  with  the  other 
eye,  and  the  difference  between  the  two  eyes  leads  to  a  constant 
error  of  setting. 

With  extremely  dim  lamps  (or  with  bright  lamps  at  great 
distances  from  the  screen  of  the  Bunsen  photometer)  the  accuracy 


mirror 


mirror 


tight  - 
from 
standard 
lamp  - 


^ 

/  I       ~~~^3 

\  \ 

\   X 

'  I    - 

\ 

screen          •<  — 

\ 

\ 

7/  ^= 

\ 
\ 
k 

/       -«  — 
4 

\    1 

\    I 

\     /  lines  of  vision 

\   1 

\l 

light 
from 
given 
lamp 


Fig.  63. 

of  setting  is  very  low ;  a  number  of  settings  taken  under  such  con- 
ditions may  deviate  from  each  other  by  several  per  cent.  With 
increasing  intensity  of  illumination  on  the  screen  the  accuracy 
of  setting  increases  and  reaches  about  one  half  of  one  per  cent, 
when  the  intensity  of  illumination  on  the  screen  is  about  one 
foot-candle  or  more.* 

FECHNER'S  RATIO. — Given  a  surface  with  intensity  of  illumination  /  and  let 
A7  be  the  added  illumination  which  is  barely  perceptible  to  the  eye.  The  ratio 
A7/7  is  called  Fechner's  ratio.  Thus  defined  this  ratio  is  approximately  equal  to 
the  percentage  accuracy  of  setting  of  a  Bunsen  photometer. 

*  The  limit  of  accuracy  of  the  setting  of  a  Bunsen  photometer  is  about  two 
tenths  of  one  per  cent.,  and  the  error  which  is  introduced  by  the  inaccuracy  of 
the  law  of  inverse  squares  should  be  considerably  less  than  two  tenths  of  one 
per  cent.  Therefore  the  maximum  dimension  of  the  luminous  surface  of  a 
lamp  should  not  exceed  about  one  twentieth  of  the  distance  of  the  lamp  from 
the  photometer  screen.  See  Art.  48. 


io8 


ELECTRIC    LIGHTING. 


The  Bunsen  photometer  screen,  together  with  the  two  mirrors 
which  are  shown  in  Fig.  63  is  usually  mounted  in  a  box  which  is 
called  a  screen  box  or  sight  box.  An  extensively  used  substitute 
for  the  Bunsen  sight  box  is  the  Lummer-Brodhun  sight  box  in 
which  an  optical  device  (a  prism-set)  is  used  for  showing  portions 
of  the  two  sides  of  a  white  opaque  screen  side  by  side  in  the 
same  field  of  view.  Two  forms  of  the  Lummer-Brodhun  prism- 
set  are  described  in  Arts.  63  and  65. 

58.  Distribution  of  light  around  a  lamp. — In  defining  the 
spherical-candle  the  idea  of  uniformity  of  distribution  of  light 


Fig.  64. 

around  a  lamp  was  introduced  for  the  sake  of  simplicity.  In 
fact,  however,  no  lamp  gives  complete  uniformity  of  distribution 
of  light,  but  the  conical  intensity  (candle-power)  is  always  greater 
in  certain  directions  and  less  in  other  directions.  Thus  curve  B, 
Fig.  64,  shows  the  distribution  of  light  around  a  tungsten  lamp, 
and  curves  E,  I  and  F  show  the  distribution  of  candle-power 


PHOTOMETRY   AND    ILLUMINATION. 


109 


around  the  same  lamp  when  it  is  equipped  with  "extensive," 
"intensive"  and  "focusing"  prismatic  glass  reflectors  respec- 
tively.* Figure  65  sjiows  the  distribution  of  light  around  an 
ordinary  carbon-filament  lamp  without  a  shade.  In  these  figures 
the  conical  intensity  (candle-power)  in  each  direction  is  repre- 
sented to  scale  by  the  length  of  the  radius  vector  of  the  curve. 


— — ^^ 

— — —  16.0! Horizontal  — 


Fig.  65. 

The  distribution  of  candle-power  about  a  lamp,  which,  like  a 
carbon-filament  lamp,  can  be  held  in  any  position,  may  be 
determined  by  mounting  the  lamp  in  a  universal  holder  at  one 
end  of  the  photometer  bar,  turning  it  step  by  step  in  various 
positions  and  taking  the  photometer  reading  for  each  position. 

In  some  cases  a  lamp  is  symmetrical  with  respect  to  an  axis 
so  that  a  complete  knowledge  of  the  distribution  of  candle-power 
about  the  lamp  may  be  obtained  by  determining  the  candle- 
power  in  different  directions  in  a  single  plane  which  contains  the 
axis  of  symmetry  of  the  lamp. 

In  many  cases,  a  lamp  is  approximately  symmetrical  with 
respect  to  an  axis,  so  that  the  slight  variations  of  candle-power 

*  These  reflectors  are  described  in  Articles  73  and  75. 


no 


ELECTRIC    LIGHTING. 


around  the  axis  of  approximate  symmetry  are  .of  no  importance. 
In  such  a  case  the  lack  of  symmetry  may  be  averaged  out,  as  it 
were,  by  rotating  the  lamp  at  a  speed  of  three  or  four  revolutions 
per  second  about  its  axis  of  approximate  symmetry  while  the 
photometer  readings  are  being  taken.  The  data  for  Figs.  64  and 
65  were  obtained  in  this  way.  The  vertical  dotted  line  in  Fig. 
65  is  the  axis  of  approximate  symmetry,  and  the  lamp  (with 
its  shade)  was  rotated  about  this  axis  while  the  various  readings 
were  taken. 

In  the  case  of  a  lamp  which  must  be  held  in  a  fixed  position, 
such  as  an  arc  lamp,  a  gas  lamp,  or  a  kerosene  lamp,  one  or  more 
mirrors  are  used  to  reflect  the  different  beams  from  the  lamp 
along  the  photometer  bar.  Thus  Fig.  66  shows  three  mirrors 

•counterpoise 

open  wheel 


axis  of 
photometer 


Fig.  66. 

arranged  to  reflect  the  light  from  a  fixed  lamp  along  a  pho- 
tometer bar.  The  three  mirrors  are  suspended  in  a  rigid  frame 
which  may  be  rotated  about  the  axis  of  the  photometer  as 
indicated  in  the  figure.  The  figure  shows  the  mirrors  in  the 
position  to  reflect  the  downward  beam  from  the  lamp  along  the 
photometer  bar. 

The  mirrors  shown  in  Fig.  66  must  be  large  enough  so  that, 
with  the  eye  placed  at  the  photometer  screen,  one  can  see  the 


PHOTOMETRY   AND   ILLUMINATION.  Ill 

entire  luminous  surface  of  the  lamp  including  the  globe  or  shade; 
and  in  using  equation  (19)  the  distance  of  the  lamp  from  the 
photometer  screen  must  be  taken  as  the  sum  of  the  distances 
/,  g,  h  and  i  in  Fig.  66. 

The  mirrors  in  Fig.  66  reflect  only  a  certain  fractional  part 
of  the  light  from  the  lamp,  and  therefore  the  photometer  reading 
must  be  multiplied  by  a  correction  factor  when  the  mirrors  are 
used.  This  correction  factor  may  be  found  by  observing  the 
photometer  readings  corresponding  to  a  certain  beam  from  the 
lamp  (a)  with  the  mirrors,  and  (b)  without  the  mirrors,  making  due 
allowance  for  the  effective  distance  from  the  lamp  to  screen  in 
each  case. 

If  it  is  feasible  the  lamp  should  be  rotated  steadily  about  the 
vertical  axis  in  Fig.  66  while  the  photometer  readings  are  being 
taken. 

Distribution  of  light  around  a  very  fine  straight  filament. — In  the  ordinary 
tungsten  lamp  the  light  is  emitted  by  a  number  of  nearly  straight  parallel  tungsten 
wires,  and  the  distribution  of  light  is  very  nearly  of  the  kind  one  would  get  from  a 
single  straight  filament. 

Let  C  be  the  candle-power  of  the  equatorial  beam  as  shown  in  Fig.  67.  If 
the  filament  is  very  fine  and  if  it  radiates  light  like  a  perfectly  diffusing  surface 
(an  illu/ninated  surface  of  plaster  for  example),  then,  according  to  Lambert's 
cosine  law,  the  candle-power  of  the  beam  b  is: 

b  =  C  cos  6  (i) 

The  sectional  intensity  of  the  beam  b  at  the  surface  of  the  reference  sphere  is 
6/r2,  according  to  equation  (14) ;  the  area  of  the  zone  zz  of  the  reference  sphere  is 
2irr  cos  &  X  r  •  A0;  and  the  amount  of  light  in  lumens  which  passes  through  the  zone 
zz  is  the  product  of  the  sectional  intensity  &/r2  and  the  area  of  the  zone.  There- 
fore 

AL    =  27TC  COS2  0  .  A0  (ii) 

whence 

L  =  2TC    I      "  cos2  0 .  d6  =  7r*C  (iii) 


in  which    L    is  the  total  amount  of  light  in  lumens  emitted  by  the  filament. 

To  find  the  mean  spherical  candle-power  of  the  filament,  divide  L  by  the  spherical 
angle  corresponding  to  the  entire  reference  sphere,  namely,    4-0".     This  gives 

Mean  spherical  )    _  ir 

candle-power  of  the  filament   j    ~~  4 


112 


ELECTRIC    LIGHTING. 


Now  the  equatorial  candle-power,  C,  corresponds  to  what  is  usually  called  the 
mean  horizontal  candle-power,  and  the  factor  by  which  the  mean  horizontal  candle- 
power  of  a  lamp  must  be  multiplied  to  give  the  mean  spherical  candle-power  is 
called  the  spherical  reduction  factor  of  the  lamp.  Therefore  the  spherical  reduction 
factor  of  a  lamp  which  has  a  fine  straight  filament  is  T/4  or  0.7854. 


/^  pole 

/  (reference 
U    sphere 

ft  radius  r 

i 


Fig.  67. 


Fig.  68. 


The  candle-power  distribution  curve  of  a  very  fine  straight  filament  is  made 
up  of  two  circles  having  the  filament  as  their  common  tangent,  as  shown  in  Fig.  68, 
and  the  diameter  of  each  circle  is  the  equatorial  candle-power,  C.  The  radius  of 
the  dotted  circle  in  Fig.  68  is  equal  to  Tr/4  X  C  and  it  represents  the  mean  spherical 
candle  power  of  the  filament. 

The  candle-power  distribution  curve  of  an  ordinary  tungsten  lamp  without  a 
shade  is  shown  by  the  curve  BB  in  Fig.  64,  and  it  is  very  similar  to  the  two  full- 
line  circles  in  Fig.  68.  The  spherical  reduction  factor  of  an  ordinary  tungsten 
lamp  should  be  nearly  equal  to  w/4.  In  fact  the  spherical  reduction  factor  of  such 
a  lamp  is  about  0.79. 

59.  Measurement  of  total  light  flux  from  a  lamp. — If  a  lamp 
were  to  emit  light  of  the  same  conical  intensity  (same  candle- 
power)  in  all  directions,  then  the  candle-power  in  any  direction 
as  measured  by  a  Bunsen  photometer  would  be  numerically  equal 
to  the  total  amount  of  light  expressed  in  spherical-candles,  and 
multiplying  by  4?r  would  reduce  to  lumens.  In  general,  how- 
ever, light  is  emitted  by  a  lamp  unequally  in  different  directions, 
and  the  amount  of  light  emitted  by  a  lamp  is  determined  by 
measuring  the  candle-power  in  every  direction  and  taking  the 
average.  This  average  is  the  amount  of  light  in  spherical- 
candles;  to  reduce  to  lumens  multiply  by  471-. 


PHOTOMETRY   AND   ILLUMINATION. 


If  the  average  is  to  be  calculated  simply  by  adding  and  dividing 
then  the  directions  in  which  the  separate  readings  are  taken 
must  be  distributed  uniformly  over  the  surface  of  a  sphere  with 
its  center  at  the  lamp.  This  sphere  is  called  the  reference  sphere 
for  the  sake  of  brevity.  If  the  readings  are  not  so  distributed, 
then  each  reading  must  be  multiplied  by  the  spherical  area  which 
may  be  properly  assigned  to  it,  and  the  sum  of  such  products  must 
be  divided  by  the  total  area  of  the  sphere  to  give  the  correct  average. 

When  a  lamp  can  be  rotated  at  a  speed 
of  three  or  four  revolutions  per  second 
about  its  axis  of  approximate  symmetry, 
the  total  light  flux  from  the  lamp  may 
be  determined  by  taking  readings  of  can- 
dle-power in  different  directions  in  one 
plane  only,  namely,  a  plane  which  in- 
cludes the  axis  of  rotation.  Thus  the 
lamp  L  in  Fig.  69  would  be  rotated  about 
the  vertical  axis  PQ,  and  the  conical 
intensities  Ci,  C-2,  Cs,  Q,  etc.,  at  equal 
angular  distances  would  be  measured. 
On  account  of  the  rotation  of  the  lamp 
each  setting  of  the  photometer  gives  the 
average  candle-power  along  a  parallel  of  latitude,  as  it  were. 
Each  of  the  readings  C\,  Cz,  C3,  Ci,  etc.,  represents,  therefore,  the 
candle-power  over  a  zone  of  the  reference  sphere.  Consequently 
the  readings  must  be  multiplied  by  the  areas  of  the  respective 
zones,  and  the  sum  of  these  products  must  be  divided  by  the 
total  area  of  the  reference  sphere  to  get  the  correct  average 
candle-power  in  all  directions,  the  mean  spherical  candle-power 
as  it  is  called. 

This  calculation  may  be  easily  understood  with  the  help  of 
Fig.  70  in  which  ccc  is  a  given  candle-power  curve,  the  curve 
shown  in  Fig.  65  for  example.  Consider  the  candle-power  which 
is  represented  by  the  radius  vector  Oa.  This  candle-power  may 
be  thought  of  as  referring  to  the  zone  zz  of  the  reference  sphere. 
9 


Fig.  69. 


114 


ELECTRIC    LIGHTING. 


Taking  the  diameter  DD  of  the  reference  sphere  as  representing 
the  total  area  of  the  sphere  then  the  height  h  of  the  zone  zz 
represents  the  area  of  the  zone.*  Therefore  the  product  Oa  X  h 
is  the  product,  candle-power  Oa  X  area  of  the  corresponding  zone, 
and  the  sum  of  all  such  products  has  to  be  divided  by  the  diameter 
DD  of  the  reference  sphere  to  give  the  mean  spherical  candle- 
power  of  the  lamp. 

It  is  especially  to  be  noted  that  the  area  enclosed  by  a  candle- 
power  distribution  curve  is  not  a  measure  of  the  total  amount  of 


reference 
sphere 

IS 


light  emitted  by  a  lamp.  Thus  each  of  the  four  candle-power 
distribution  curves  in  Fig.  64  represents  approximately  the  same 
total  amount  of  light,  indeed  each  of  the  curves  EE,  II  and  FF 
represents  only  about  88  per  cent,  as  much  light  as  curve  BB. 
60.  Rousseau's  diagram. — When  the  observed  candle-powers 
of  a  lamp  correspond  to  zones  of  the  reference  sphere  as  above 

*  That  is,  the  rule  for  finding  the  area  of  a  spherical  zone  is  to  multiply  the  entire 
area  of  the  sphere  (47rr2)  by  h/D,  where  h  is  the  altitude  of  the  zone  and  D 
is  the  diameter  of  the  sphere. 


PHOTOMETRY   AND    ILLUMINATION.  115 

explained,  then  the  multiplication  of  each  candle-power  by  the 
area  of  the  corresponding  zone,  the  adding  of  these  products 
together,  and  the  dividing  of  the  total  sum  by  the  area  of  the 
reference  sphere  may  be  done  graphically.  The  most  familiar 
graphical  method  is  due  to  Rousseau,  and  the  drawing  which  is 
necessary  to  carry  it  out  is  called  Rousseau's  diagram. 

The  curve  ccc,  Fig.  71,  is  the  given  candle-power  curve  (like 
Fig.  65,  for  example).  Construct  another  curve  c'c'c' ',  Fig.  72, 
such  that  each  abscissa  O'a'  is  equal  to  the  corresponding  radius 


• 


FIG.  71. 


Fig.  72. 


vector  Oa.  The  candle-power  Oa  multiplied  by  the  area  of 
the  corresponding  zone*  is  evidently  the  same  thing  as  O'a' 
multiplied  by  h,  and  this  product  is  equal  to  the  shaded  area  in 
Fig.  72.  Consequently,  the  sum  of  all  such  products  is  equal  to 
the  total  area  between  the  curve  c'c'c'  and  the  axis  D'D'. 
Therefore  this  area  can  be  measured  by  a  planimeter  and  divided 
by  the  distance  D'D'  (the  diameter  of  the  reference  sphere)  to 
give  the  true  mean  spherical  candle-power  of  the  lamp. 

*  See  discussion  of  Fig.  70  in  Art.  59. 


n6 


ELECTRIC   LIGHTING. 


Other  graphical  methods  have  been  proposed  for  the  determina- 
tion of  mean  candle-power  by  Kennelly*  and  by  Wohlauer.f 

61.  The  flicker  photometer. — The  flicker  photometer  is  a 
device  for  eliminating,  to  some  extent,  the  error  in  the  setting 
of  a  photometer  which  is  due  to  differences  in  color  of  the  lamps 
which  are  being  compared.  The  following  is  the  principle  upon 
which  the  elimination  of  color  error  is  based.  When  one  looks 
at  a  thing  such  as  a  photometer  screen  one  has  a  sensation  of 


light  from_ 
standard  ££ 
lamp 


light  from 
_r^.±:  m    given 
lamp 


brightness  and  a  sensation  of  color.  Both  of  these  sensations 
persist  for  an  appreciable  interval  of  time  after  stimulation 
ceases,  but  the  sensation  of  color  persists  much  longer  than  the 
sensation  of  brightness.  Therefore  if  the  two  sides  of  the  pho- 
tometer screen  are  brought  into  the  same  field  of  view  in  rapid 
succession  (with  high  frequency  of  interchange),  the  color  sensa- 

*  See  Electrical  World,  March  28,  1908. 

t  See  Illuminating  Engineering,  Vol.  Ill,  page  655. 


PHOTOMETRY   AND   ILLUMINATION.  117 

tion  produced  by  the  two  sides  of  the  screen  and  also  the  brightness 
sensation  produced  by  the  two  sides  of  the  screen  will  both  become 
perfectly  steady  (devoid  of  flicker),  whereas  a  much  lower  fre- 
quency of  interchange  will  suffice  to  give  a  steady  color  sensation 
but  leave  a  flickering  sensation  of  brightness  unless  the  two  sides 
of  the  screen  have  the  same  brightness.  Therefore  if  we  use  a 
frequency  of  interchange  just  sufficient  to  give  a  steady  color 
sensation,  the  two  sides  of  the  photometer  screen  can  be  brought 
to  equality  of  brightness  by  adjusting  the  photometer  until  the 
brightness-flicker  disappears.  The  various  flicker  photometers 
differ  in  the  arrangement  used  for  bringing  about  the  rapid  inter- 
change of  the  two  sides  of  the  photometer  screen  in  the  same 
field  of  view,  and  the  most  satisfactory  device  is  perhaps  that 
due  to  Marten.*  The  two  faces  of  a  prism  of  white  plaster  S, 
Fig.  73,  are  illuminated  by  the  standard  lamp  and  a  given  lamp 
respectively.  The  eye  is  focused  upon  one  of  the  illuminated 
faces  of  the  plaster  prism  by  means  of  the  lens  LL,  and  the  thin 
glass  prism  P  which  is  carried  in  a  rotating  holder  HH  directs 
one's  vision  to  one  face  and  then  to  the  other  face  of  the  plaster 
prism  in  rapid  succession.  This  arrangement  constitutes  a  sight 
box,  and  it  is  used  on  a  photometer  bar  in  the  same  way  as  the 
Bunsen  sight  box,  as  explained  in  Art.  57. 

Another  form  of  flicker  sight-box  which  is  quite  satisfactory  is 
that  of  Simmance  and  Abady.f 

62.  The  complete  photometer;  laboratory  type. — The  photom- 
eter consists  of  a  sight-box  moving  along  a  track  or  bar,  and 
the  lamps  to  be  compared  are  placed  at  the  ends  of  this  bar. 
The  sight-box  may  be  of  the  Bunsen  type  as  described  in  Art. 
57,  or  of  the  Lummer-Brodhun  type  as  described  in  Arts.  63  and 
65,  or  a  sight-box  of  the  flicker- type  may  be  used  as  described  in 
Art.  61.  Usually  the  photometer  setting  is  made  by  moving  the 

*  This  flicker  photometer  is  manufactured  by  Schmidt  and  Haensch,  of  Berlin. 

t  The  Simmance-Abady  flicker  sight-box  is  described  on  pages  491-492  of  Vol. 
I,  Johns  Hopkins  University  Lectures  on  Illuminating  Engineering,  Johns  Hopkins 
Press,  1911. 


118  ELECTRIC   LIGHTING. 

sight-box  along  the  photometer  bar,  but  sometimes  it  is  more 
convenient  to  make  the  setting  by  moving  the  standard  lamp 
as  in  the  Sharp-Millar  portable  photometer  (see  Art.  63). 

The  essential  features  of  the  laboratory  type  of  photometer 
are  shown  in  Fig.  74.     Dead  black  surfaces  BB  are  placed  back 

top  view  of  photometer 
D\  sight  box  \D       \D       \D 


standard  lamp 


tgioen  lamp    O 


Fig.  74. 

of  each  lamp,  and  a  series  of  black  diaphragms  DD  are  placed 
so  as  to  shield  the  photometer  screen  and  the  observer's  eyes 
from  all  stray  light.  Freshly  brushed  black  velvet  is  the  best 
material  to  use  for  these  diaphragms  and  for  the  back  pieces  BB. 

The  law  of  inverse  squares  is  assumed  in  the  use  of  a  photom- 
eter, as  explained  in  Art.  57,  and  therefore  the  distance  from  the 
photometer  screen  to  either  lamp  should  never  be  less  than  about 
20  times  the  maximum  dimension  of  the  luminous  surface  of  the 
lamp.  A  lo-foot  photometer  bar  is  therefore  suitable  for  use 
with  ordinary  bare  incandescent  lamps,  but  when  a  lamp  has  a 
large  shade  the  bar  should  be  much  longer  because  the  shade  is, 
in  effect,  the  luminous  source.  The  short  distance  between  the 
standard  lamp  and  the  photometer  screen  in  the  Sharp-Millar 
photometer  (see  next  article)  is  permissible  because  of  the  small 
size  of  the  standard  lamp. 

It  is  best  to  set  up  the  photometer  in  a  dark  room  with  dead 
black  walls,  but  if  the  back  curtains  BB  and  the  diaphragms  DD 
are  properly  arranged  the  photometer  room  may  be  dimly  lighted 
without  interfering  with  accurate  photometric  work. 

Tables  should  be  arranged  at  the  ends  of  the  photometer  bar 


PHOTOMETRY   AND    ILLUMINATION.  119 

for  the  gas  or  electric  meters  and  other  accessory  apparatus,  such 
as  pressure  regulators  (for  gas)  and  rheostats  and  switches  (for 
electric  current).  „ 

A  single  photometer  setting  is  apt  to  be  considerably  in  error, 
and  therefore  a  number  of  settings  is  taken  whenever  possible. 
The  taking  of  a  set  of  readings  is  greatly  facilitated  by  placing 
a  strip  of  paper  on  the  photometer  bar  and  marking  the  succes- 
sive positions  of  the  photometer  screen  for  a  series  of  readings; 
this  marking  may  be  done  very  quickly  by  a  pencil  point  which 
is  carried  by  a  flat  spring  attached  to  the  sight-box  of  the 
photometer. 

A  photometer  for  incandescent  lamp  tests  is  usually  provided 
with  a  universal  rotating  holder  so  that  the  lamp  under  test  can 
be  kept  rotating  and  the  axis  of  rotation  can  be  given  any  desired 
position. 

It  is  important  to  use  a  storage  battery7  for  supplying  current 
to  electric  lamps  under  test  because  other  sources  of  supply  are 
usually  subject  to  sudden  changes  of  voltage.  When  a  storage 
battery  is  not  available  the  standard  lamp  and  the  lamp  under 
test  should  both  be  operated  from  the  same  mains  so  that  both 
lamps  may  be  affected  to  approximately  the  same  degree  by 
voltage  variation. 

63.  The  portable  photometer  and  illuminometer. — The  most 
extensively  used  portable  photometer  is  perhaps  the  Weber 
photometer  *  The  essential  features  of  this  instrument  are  em- 
bodied in  the  more  recent  and  improved  portable  photometer  of 
Sharp  and  Millar,  and  it  is  therefore  sufficient  to  explain  the 
construction  and  use  of  the  Sharp-Millar  instrument  which  can 
be  used  for  measuring  the  candle-power  of  any  lamp  in  service 
or  for  the  measurement  of  the  intensity  of  illumination  at  any 
point  on  a  street  or  in  a  room.  The  essential  features  of  the 
Sharp-Millar  photometer  are  shown  in  Figs.  75  and  76. 

The  observer's  eye  is  focused  on  the  diagonal  plane   ffoia. 

*  See  Industrial  Photometry,  pages  85-91.  Palaz  (translated  by  G.  W.  and  M. 
R.  Patterson),  Van  Nostrand,  1894. 


120 


ELECTRIC   LIGHTING. 


Lummer-Brodhun  prism  set  L-B,  and  this  diagonal  plane  is  the 
field  of  view  of  the  observer.  Through  the  center  of  the  field  of 
view  (where  the  prisms  are  in  contact)  the  observer  sees  the  dif- 
fusing plate  DD  in  Fig.  75,  or  the  translucent  milk-glass  plate 


-light  from  test  lamp 


comparison 
lamp 


Fig.  75. 

SfSr  in  Fig.  76;  and  through  the  edge  portions  of  the  field  of 
view  (where  the  prisms  are  not  in  contact)  the  observer  sees  the 
translucent  milk-glass  plate  55  which  is  illuminated  by  the 
comparison  lamp  (standard  lamp)  in  the  instrument. 


light  from  all  parts  of  rowf 


comparison 
lamp 


To  set  the  photometer  the  comparison  lamp  is  moved  towards 
or  away  from  55  until  the  central  and  edge  portions  of  the 
field  of  view  are  equally  bright,  and  the  reading  of  the  instrument 
is  the  distance  of  the  comparison  lamp  from  55.  To  interpret 
the  reading  of  the  instrument  calibration  is  necessary  as  follows : 


PHOTOMETRY   AND   ILLUMINATION.  121 

(a)  Calibration  for  candle-power. — A  series  of  lamps  of  known 
candle-powers  are  placed  in  succession  at  a  chosen  distance   d 
from  DD  (in  place  of  the  test  lamp  in  Fig.  75),  the  corresponding 
readings  of  the  photometer  are  taken,  and  a  curve  is  plotted 
showing  readings  as  abscissas  and  candle-powers  as  ordinates. 
Then  if  the  lamp  to  be  tested  is  at  a  distance  dr  from   DD,   the 
candle-power  of   the  lamp  is    (d'/d)2    times   the  candle-power 
which  is  given  by  the  curve. 

(b)  Calibration  for  intensities  of  illumination  on  S'S'. — A  lamp 
of  known  candle-power  is  placed  at  a  series  of  measured  distances 
from     S'S'     in  Fig.  76,  thus  producing  known  intensities  of 
illumination  upon  S'S' ;  the  corresponding  readings  of  the  pho- 
tometer are  taken;  and  a  curve  is  plotted  showing  readings  as 
abscissas  and  foot-candles  as  ordinates.     Then  to  determine  the 
intensity  of  illumination  of,  say,  a  horizontal  surface  at  a  given 
point  in  a  room,  the  photometer  is  set  up  with  the  plate    S'S' 
at  the  given  point  and  horizontal,  the  photometer  reading  is 
taken,  and  the  desired  value  of  the  intensity  of  illumination  is 
found  from  the  curve. 

The  commercial  form  of  the  Sharp-Millar  photometer  is  usually 
provided  with  a  direct-reading  scale,  but  it  should  be  occasionally 
calibrated  as  above  explained. 

The  comparison  lamp  is  a  very  small  tungsten  lamp  which  has 
been  thoroughly  aged  before  it  is  mounted  in  the  instrument, 
and  the  voltage  between  the  terminals  of  the  comparison  lamp  is 
kept  at  a  prescribed  value. 

The  Sharp-Millar  photometer  as  furnished  by  the  manufac- 
turers* is  provided  with  a  smokefglass  plate  which  can  be  placed 
at  p  if  very  dim  illumination  is  to  be  measured  or  at  p'  if  very 
bright  illumination  is  to  be  measured.  This  smoke-glass  is 
usually  adjusted  by  the  manufacturers  so  that  when  used  at  p 
the  photometer  reading  (in  case  the  photometer  is  direct  reading) 
must  be  divided  by  10,  and  when  used  at  p'  the  photometer 
reading  must  be  multiplied  by  10. 

*  Foote,  Pierson  &  Co.,  of  New  York  City. 


122 


ELECTRIC    LIGHTING. 


Figure  77  shows  the  arrangement  of  the  Sharp-Millar  photom- 
eter. The  containing  box  is  blackened  inside,  and  a  series  of 
diaphragms  like  DD,  Fig.  74,  are  arranged  between  the  com- 
parison lamp  L  and  the  translucent  screen  55.  The  elbow 
tube  T  can  be  turned  so  that  its  end  E  points  in  any  desired 
direction.  The  translucent  plate  S'S'  is  placed  over  the  end  E, 
and  DM  is  a  plate  of  which  one  face  is  ground  milk-glass  for 
diffusion,  and  the  other  face  is  a  thin  plate  of  clear  polished 
glass  backed  with  silver  (a  mirror).  The  mirror  face  is  used  in 
Fig.  76  and  the  ground  milk-glass  face  is  used  in  Fig.  75. 


*    side  view 
part  section 


top  view 
section 


H 

Fig.  77. 

An  interesting  use  of  the  Sharp-Millar  photometer  is  to  turn 
the  mirror  face  of  DM  outward  as  in  Fig.  76,  remove  the  milk- 
glass  plate  S'S'  so  as  to  leave  the  end  E  of  the  elbow  tube  open, 
and  direct  the  open  end  of  the  elbow  tube  towards  a  piece  of 
uncalendered  white  paper  which  faces  a  lamp  to  be  tested.  The 
photometer  reading  is  taken  for  a  lamp  of  known  candle-power 
at  distance  d  from  the  paper  screen,  and  then  the  candle-power 
of  any  given  lamp  is  (df  /d)2  times  the  photometer  reading 
(photometer  thought  of  as  being  direct  reading  for  the  sake  of 
simplicity  of  statement),  where  d'  is  the  distance  of  the  given 
lamp  from  the  paper  screen.  This  result  is  independent  of  the 
distance  of  the  piece  of  white  paper  from  the  instrument,  and  if 


PHOTOMETRY   AND    ILLUMINATION. 


123 


the  paper  is  free  from  gloss  the  result  is  independent  of  obliquity 
of  vision  of  the  white  paper  as  seen  from  the  end  of  the  elbow 
tube  of  the  instrument.  The  piece  of  white  paper  must  face  the 
lamp  to  be  tested  and  it  must  be  large  enough  to  completely  fill  the 
central  part  of  the  observer's  field  of  view  (where  the  Lummer- 
Brodhun  prisms  are  in  contact  in  Fig.  76).  This  use  of  the 
Sharp-Millar  photometer  furnishes  a  striking  illustration  of  the 
two  propositions  (a)  and  (b)  in  Art.  53. 

64.  The  globe  photometer  of  Ulbricht.* — Several  types  of 
photometer  for  determining  the  mean  spherical  candle-power  of 
a  lamp  by  a  single  setting  of  the  photometer  have  been  devised. 
The  most  notable  are  perhaps  the  integrating  photometers  of 
C.  P.  Matthews,!  but  the  Ulbricht  globe  photometer  is  the  most 
convenient  in  use.  The  ar- 
rangement of  this  photometer 
is  shown  in  Fig.  78;  A  A  and 
BB  are  two  hemispheres  on 
wheel-bases  so  that  they  can 
be  easily  moved  apart.  The 
interior  of  these  hemispheres  is 
painted  with  a  dead -white  paint 
(a  white  paint  free  from  gloss)  4 

The  lamp  to  be  tested  and  a 
' '  comparison  lamp '  'of  which  the 
mean  spherical  candle-power  Fi  78 

has  been  previously  determined 

are  hung  in  the  sphere  as  shown  in  the  figure.  A  small  milk-glass 
diffusing  window  S'S'  is  placed  in  one  side  of  the  sphere  and 

*  The  globe  photometer  is  fully  described  and  the  results  of  a  thorough  inves- 
tigation of  its  reliability  are  given  by  L.  Bloch  in  Electrotechnische  Zeitschrift, 
pages  1047-1052  and  1074-1078,  November  16  and  23,  1905.  See  also  a  paper 
on  the  Ulbricht  integrating  sphere  by  C.  H.  Sharp,  Johns  Hopkins  University, 
Lectures  on  Illuminating  Engineering,  Vol.  I,  pages  481-485,  Baltimore,  1911. 

f  See  Transactions  of  the  American  Institue  of  Electrical  Engineers,  Vol.  XVIII, 
pages  677-697,  1901;  and  Vol.  XX,  pages  59-70,  1902. 

J  The  most  satisfactory  paint  is  barium  sulphate  in  zapon  lacquer. 


124 


ELECTRIC    LIGHTING. 


shaded  from  the  direct  light  of  the  lamps  by  two  white  card- 
board screens  kk.  The  milk-glass  diffusing  window  S'S'  is  the 
illumination  plate  of  a  Sharp-Millar  photometer  (the  same  as 
S'S'  in  Fig.  76).  The  photometer  reading  is  taken  with  the 
"comparison  lamp"  in  place.  This  lamp  is  then  extinguished, 
the  lamp  to  be  tested  is  lighted,  and  the  photometer  reading  is 
again  taken.  Multiplying  the  known  mean  spherical  candle- 


1.8 


1.6 


1.4 


0.8 


0.6 


0.4 


D 


\  cave  length 


0.5 


0.7 


Fig.  79. 

CC,  carbon-filament  lamp;  TTt   tungsten-filament  lamp  ;  A  A,  carbon-arc  lamp; 

DD,  daylight. 

power  of  the  "comparison  lamp"  by  the  ratio  of  the  two  pho- 
tometer readings  gives  the  mean  spherical  candle-power  of  the 
lamp  under  test.  In  this  statement  the  photometer  is  assumed 
to  be  direct  reading. 


PHOTOMETRY   AND    ILLUMINATION. 


125 


65.  The  spectrophotometer  is  a  combination  of  a  spectroscope  and  a  photom- 
eter arranged  for  comparing  the  intensities  of  two  beams  of  light,  wave-length  by 
wave-length.  Figure  79  ^shows  the  results  of  a  spectroscopic  comparison  of  the 
light  from  a  carbon-filament  lamp  (curve  C),  the  light  from  a  tungsten-filament 
lamp  (curve  T),  and  the  light  from  the  crater  of  a  carbon-arc  lamp  (curve  A),  each 
with  daylight  (curve  D}.  The  meaning  of  these  curves  is  as  follows:  For  the  same 
intensity  at  the  sodium  line  (wave-length  0.589  millionth  of  a  meter),  the  light  from 
the  carbon-filament  glow  lamp  is  1.93  times  as  bright  as  daylight  in  the  extreme 
red  and  0.36  as  bright  as  daylight  in  the  extreme  violet;  for  the  same  brightness  at 
the  sodium  line,  the  light  from  the  hot  carbon  tips  of  the  carbon-arc  lamp  is  1.2 
times  as  bright  as  daylight  in  the  extreme  red  and  0.45  as  bright  as  daylight  in 
the  extreme  violet 

One  of  the  best  forms  of  spectrophotometer  is  the  spectrophotometer  of  Lummer 
and  Brodhun,  the  essential  features  of  which  are  shown  in  Fig.  80,  in  which  L-B 
is  a  Lummer- Brodhun  prism-set.  The  observer's  eye,  placed  at  the  narrow  slit 


Fig.  80. 


E,  looks  through  the  lens  TT  and  the  glass  prism  P  and  is  focused  on  the  diagonal 
face  ff  of  the  Lummer- Brodhun  set  so  that  this  diagonal  face  is  the  observer's 
field  of  view.  The  observer  sees  the  central  portion  of  the  field  of  view  illuminated 
by  light  of  one  wave-length  from  the  diffusing  plate  G,  whereas  the  edge  por- 
tions of  the  field  of  view  are  illuminated  by  light  of  the  same  wave-length  from 
the  diffusing  plate  F.  The  two  diffusing  plates  F  and  G  are  illuminated  by 
the  comparison  lamp  and  the  test  lamp,  respectively,  and  the  distances  D  and  Df 
are  adjusted  until  the  observer's  field  of  view  is  uniformly  illuminated.  Then  the 
ratio  of  brightness  of  the  two  lamps  for  the  given  wave-length  is  equal  to  the  ratio 
of  the  squares  of  the  distances  D  and  Df.  In  some  forms  of  the  Lummer-Brodhun 
spectrophotometer,  the  observer's  field  of  view  is  brought  to  uniform  intensity 
qf  illumination  by  adjusting  the  widths  of  the  two  slits  5  and  •$'.. 


CHAPTER  V. 


anode 


ELECTRIC  LAMPS.     LAMP  SHADES  AND  REFLECTORS. 

66.  The  electric  arc.  The  arc  lamp. — When  two  carbon  or 
metal  rods  are  connected  to  supply  mains,  brought  into  contact* 
and  then  separated,  the  current  flows  across  the  gap  between  the 
ends  of  the  rods  producing  what  is  called  an  electric  arc.  Thus 
Fig.  8 1  shows  the  appearance  of  a  direct-current  arc  between 

carbon  rods.  The  direc- 
tion of  flow  of  the  current 
is  indicated  by  the  arrow. 
The  column  of  hot  conduct- 
ing vapor  is  called  the  arc 
stream,  and  the  carbon  or 
metal  rods  are  called  the 
electrode's  (anode  and  cath- 
ode), as  shown  in  Fig.  81. 

The  arc  between  pure 
carbon  electrodes  is  called 
the  carbon  arc,  and  an  arc 
lamp  in  which  pure  carbon 
electrodes  are  used  is  called 
a  carbon-arc  lamp.  Nearly 
all  of  the  light  of  a  carbon- 
arc  lamp  comes  from  the 
hot  tips  of  the  carbons,  in- 
deed the  greater  portion  of 
the  light  comes  from  the  slightly  concave  end  of  the  anode  car- 
bon. The  arc  stream  gives  off  a  pale  violet  light. 

The  arc  between  metal  electrodes  or  between  electrodes  con- 
taining metallic  oxides  or  salts  is  called  the  luminous  arc,  because 

*  A  rheostat  must  be  included  in  the  circuit. 

126 


cathode 


Fig.  81. 


LAMPS,   LAMP   SHADES   AND    REFLECTORS. 


127 


the  arc  stream  itself  gives  off  a  great  deal  of  light.  In  this  case 
the  electrodes  are  not  intensely  heated  and  they  do  not  give  off 
any  appreciable  amount  of  light.  An  arc  lamp  in  which  a 
luminous  arc  is  used  is  called  a  luminous-arc  lamp.  The  luminous 
arc  stream  gives  off  a  smoke  or  cloud  of  condensed  metal  oxide, 
and  a  flow  of  air  must  be  maintained  through  the  arc  chamber 
of  a  luminous-arc  lamp  to  carry  away  this  oxide.  Otherwise  an 


Q  4  8  i*  i<5  20  24, 

Fig.  82. 
Curve  a  refers  to  arc  2.76  inches  long. 

"      6      '    2.36       " 

"      c      "       "     "    1.97       " 
"      d      "      "    "    1.58      " 

"      e      ' 1.18      " 

"      /      '    0.79      " 

"       g      "       "     "    0.39       " 

opaque  deposit  would  form  on  the  inner  walls  of  the  enclosing 
glass  globe. 

The  electric  arc  between  pure  carbon  rods  or  between  carbon 
rods  impregnated  with  metallic  salts  can  be  maintained  by  direct 
current  or  by  alternating  current;  but  it  is  not  practicable  to 
maintain  an  alternating-current  arc  when  either  of  the  electrodes 
is  of  metal.  Apparently  the  cathode  of  an  arc  must  be  at  a 


128 


ELECTRIC   LIGHTING. 


line  wire 


temperature  sufficiently  high  to  vaporize  the  cathode  material, 
and  with  a  massive  metal  electrode  the  heat  is  taken  away  so 
rapidly  that  the  necessary  rise  of  temperature  is  not  produced 
unless  a  very  large  current  is  used.* 

An  important  property  of  the  electric  arc  is  that  the  voltage 
across  the  arc  decreases  with  increasing  current,  as  shown  by  the 
curves  in  Fig.  82.  Consequently  it  is  necessary  to  place  resist- 
ance in  series  with  an  arc  lamp  which  is  connected  across  constant- 
voltage  supply  mains.  Without  this  resistance  the  current 
would  increase  indefinitely  and  the  arc  would  constitute  a  short 
circuit  of  the  system.  This  resistance  is  called  a  ballast  resistance, 
and  the  loss  of  energy  in  the  ballast  resistance  is  usually  about 
30  per  cent,  of  the  total  energy  delivered  by  the  supply  mains. 

In  an  alternating-current 
arc  lamp  a  choke  coil  (an 
inductance)  can  be  used  as 
a  ballast.  In  a  direct-cur- 
rent arc  lamp  a  resistance 
must  .be  used  as  ballast. 
When  arc  lamps  are  con- 
nected in  series  to  a  con- 
stant-current supply,  no 
ballast  is  necessary. 

An  important  part  of  an 
arc  lamp  is  the  mechanism  for  automatically  moving  the  elec- 
trodes so  as  to  keep  the  arc  steady.  Thus  Fig.  83  shows 
the  essential  features  of  an  arc-lamp  mechanism  for  lamps 
which  are  to  be  connected  in  series.  A  very  small  portion  of 
the  current  flows  through  a  shunt  coil  B  without  passing 
through  the  arc,  and  the  remainder  of  the  current  flows  through 
the  coil  A  and  thence  through  the  arc.  An  iron  rod  AB  pass- 
ing loosely  into  the  coils  A  and  B  is  attached  to  one  end  of 

*  For  a  discussion  of  the  physics  of  the  electric  arc  see  C.  P.  Steinmetz,  Trans- 
actions of  International  Electrical  Congress,  Vol.  II,  pages  710-730,  St.  Louis,  1904. 
Also  see  W.  R.  Whitney,  Transactions  of  American  Electrochemical  Society,  Vol, 
YII,  pages  291-299,  1905. 


Fig.  83. 


LAMPS,   LAMP   SHADES   AND    REFLECTORS.  129 

a  lever  which  is  pivoted  at  its  center,  and  the  other  end  of 
the  lever  is  provided  with  a  clutch  c  through  which  a  smooth 
brass  rod  bb  passes,  This  brass  rod  supports  one  of  the  carbon 
electrodes,  and  the  clutch  is  so  constructed  that  it  releases  the 
rod  bb  when  the  iron  rod  AB  is  raised,  thus  allowing  the  carbons 
to  come  together.  Each  of  the  coils  A  and  B  acts  to  pull  the 
rod  AB  into  itself,  and  a  spring  which  is  attached  to  the  lever 
is  adjusted  so  that  when  the  arc  is  burning  properly  the  combined 
action  of  this  spring  and  the  two  coils  A  and  B  holds  the  lever 
in  such  a  position  that  the  clutch  clasps  the  brass  rod  bb.  As 
the  arc  continues  to  burn  the  carbons  are  slowly  consumed, 
causing  the  gap  between  the  carbon  tips  to  widen.  This  increases 
the  voltage  across  the  arc  and  causes  a  greater  portion  of  the 
current  to  flow  through  the  shunt  coil  B,  which  pulls  up  on  the 
iron  rod  AB,  moves  the  lever,  lowers  the  carbon  and  ultimately 
releases  the  clutch  so  as  to  allow  the  rod  bb  to  fall.  The  carbons 
usually  come  too  near  together  when  the  clutch  c  is  thus  re- 
leased, but  the  current  in  coil  B  is  thereby  greatly  reduced  so 
that  the  current  in  coil  A  quickly  pulls  the  lever  down  and  sepa- 
rates the  carbons  to  the  desired  extent. 

67.  Carbon-arc  lamps.  The  open-arc  lamp  and  the  enclosed- 
arc  lamp. — In  the  oldest  form  of  arc  lamp  the  carbons  are  exposed 
to  the  open  air  or  surrounded  by  a  glass  globe  through  which  the 
air  circulates  freely.  This  type  of  lamp  is  called  the  open-arc 
lamp.  The  carbons  in  this  type  of  lamp  are  consumed  rapidly 
by  the  oxygen  of  the  air,  and  the  lamp  must  be  trimmed,  that 
is,  the  carbons  must  be  renewed,  about  once  in  12  hours. 

In  the  endosed-arc  lamp  the  ends  of  the  carbon  rods  project 
into  a  small  glass  bulb  which  is  very  nearly  air-tight.  In  this 
type  of  lamp  the  carbons  last  about  150  hours. 

The  carbon-arc  lamp  operates  satisfactorily  on  direct-current 
circuits  or  on  alternating-current  circuits.  The  mechanism  is, 
however,  slightly  different  in  the  two  cases  so  that  an  arc  lamp 
which  has  been  designed  especially  for  direct  current  will  not 
operate  satisfactorily  with  alternating  current. 
10 


130  ELECTRIC    LIGHTING. 

The  carbon-arc  lamp  is  rapidly  going  out  of  use.  Tungsten 
lamps  are  much  better  and  cheaper  where  small  units  are  needed, 
and  luminous-arc  lamps  and  mercury-vapor  lamps  are  much 
more  efficient  where  large  units  are  needed. 

68.  Luminous-arc  lamps.    The  magnetite-arc  lamp  and  the 

flame-arc    lamp.  —  In  the    magnetite-arc    lamp  the  anode  is  a 

short  rod  of  copper  as  shown  in  Fig.  84,*  and  the  cathode  is 

composed  of  a  mixture  of  iron  oxide  (mag- 

1  copper  netite),  titanium  oxide  and  chromium  ox- 

anode  ' 

-f  ide.     The  copper  anode  remains  relatively 

— 

t  arc  stream        cool  and  wears  away  with  extreme  slowness. 

—  The  end  of  the  cathode  is  heated  to  a  mod- 

magnetite  ,     ,  .   .  ,  , 

cathode  erately  high  temperature  during  the  opera- 

tion of  the  lamp,  and  the  oxides  are  slowly 
vaporized  producing  an  intensely  luminous 
Fig.  84.  arc*    The  copper  anode  lasts  five  thousand 

hours  or  more,  and  the  rod  of  magnetite 

lasts  about  one  hundred  and  fifty  hours.  The  light  emitted 
by  the  lamp  is  a  brilliant  white.  It  is  not  feasible  to  operate 
the  magnetite-arc  lamp  by  alternating  current. 

In  the  flame-arc  lamp  carbon  rods  are  used  as  electrodes,  and 
these  carbon  rods  are  impregnated  with  metallic  salts.  In  the 
familiar  flame-arc  lamp,  which  gives  an  extremely  brilliant  yellow 
light,  the  carbons  are  impregnated  with  calcium  fluoride 

The  flame  arc  gives  off  a  cloud  of  oxide,  and  it  is  impracticable 
to  enclose  the  flame  arc  in  a  small  bulb  such  as  is  used  in  the 
enclosed  carbon-arc  lamp.  Therefore  when  the  flame-arc  lamp 
was  first  brought  out  the  arc  was  not  enclosed  and  the  carbons 
burned  away  rapidly.  Consequently  very  long  carbons  were 
required  for  a  1 2-hour  run,  and  the  use  of  long  carbons  led  to  the 
arrangement  shown  in  Fig.  85.  This  type  is  called  the  short- 

*  Figure  84  shows  the  arrangement  of  the  electrodes  in  the  General  Electric 
Company's  lamp.  In  the  Westinghouse  magnetite-arc  lamp  the  magnetite  cathode 
is  above  and  the  anode  is  below. 


LAMPS,   LAMP   SHADES   AND    REFLECTORS.  131 

burning  inclined-carbon  flame-arc  lamp.  It  is  now  practically 
obsolete.  The  objection  to  this  type  of  flame-arc  lamp  is  the 
cost  of  the  frequent^trimming. 


carbon  rod 


oxide  ) 
deposit 


carbon  rod 


porcelain 


arc  stream 


Fig.  85. 


A  satisfactory  enclosed  flame-arc  lamp  was  placed  on  the 
market  in  1911,  the  cloud  of  oxide  from  the  arc  stream  being 
carried  by  a  natural  draft  into  a  condensing  chamber  where  the 
oxide  is  deposited,  and  the  clear  cooled  air  retuns  to  the  arc 
chamber,  but  no  fresh  air  has  access  to  the  arc  chamber.  In  the 
enclosed  flame-arc  lamp  the  carbon  electrodes  are  placed  ver- 
tically one  over  the  other  as  in  the  ordinary  carbon-arc  lamp, 
and  the  electrodes  last  about  100  hours. 

The  flame-arc  lamp  can  be  operated  either  by  direct  current 
or  by  alternating  current. 

69.  The  mercury- vapor  lamp. — In  1860  it  was  known  that  a 
steady  and  brilliantly  luminous  effect  could  be  obtained  by 
passing  an  electric  current  through  a  glass  tube  containing  mer- 
cury vapor,  and  in  1881  the  proposal  was  made  to  utilize  this 
effect  in  an  electric  lamp.  In  the  early  attempts  to  produce  a 


132 


ELECTRIC    LIGHTING. 


practicable  mercury-vapor  lamp  the  necessary  cooling  of  the 
vapor  tube  was  accomplished  by  the  circulation  of  water,  and  it 
was  not  until  Peter  Cooper  Hewitt  (about  1898)  designed  a 
vapor  tube  with  enlarged  condensing  chambers  (which,  indeed, 
do  not  need  to  be  very  large  on  a  long  tube)  that  the  mercury- 
vapor  lamp  became  a  success. 

The  essential  features  of  the  Cooper-Hewitt  lamp  are  shown 
in  Fig.  86.     A  long  glass  tube  with  a  bulb  on  each  end  is  provided 

supply  mains 


switch 


j  j  OCVtt'Vf* 

'  ^— ww^mooQ^ 


anode 


Hg 


cathode 


Fig.  86. 


with  sealed-in  lead-wires  one  of  which  connects  with  an  electrode 
(the  anode)  of  iron  or  graphite  and  the  other  connects  with  a  pool 
of  mercury  (the  cathode).  The  air  is  removed  from  the  tube 
by  an  air  pump. 

To  start  the  lamp  the  tube  is  brought  into  a  horizontal  position 
so  that  a  thread  of  mercury  bridges  across  from  electrode  to 
electrode,  the  tube  is  then  brought  back  to  an  inclined  position 
and  when  the  thread  of  mercury  breaks  the  current  continues  to 
flow  through  the  mercury  vapor.*  A  ballast  resistance  R  is 
necessary,  and  an  inductance  (a  choke  coil)  L  is  used  to  prevent 
the  stoppage  of  current  by  a  momentary  drop  of  the  supply 
voltage. 

The  type  of  lamp  which  is  started  by  tilting  is  provided  with 
a  mechanism  in  which  an  electromagnet  automatically  tilts 

*  A  momentary  high  voltage  produced  by  a  spark-coil  is  sometimes  used  for 
starting  the  flow  of  current  through  the  mercury-vapor  lamp. 


LAMPS,   LAMP   SHADES   AND    REFLECTORS.  133 

the  tube  and  brings  it  back  to  the  running  position  when  the 
control  switch  is  closed.     A  general  view  of  a  Cooper-Hewitt 
lamp  of   this  type,*  with  its  in  verted- trough  reflector  is  shown 
in  Fig.  87.     The   ballast  and   the 
tilting    mechanism  are    contained 
in  the  sheet-metal  case  above  the 
lamp  tube. 

The  simple  form  of  Cooper- 
Hewitt  lamp  cannot  be  operated 
by  alternating  current.  The  alter- 
nating-current lamp  has  two  an- 
odes and  its  connections  are  similar 
to  the  connections  of  the  mercury-  Fig.  87. 

vapor   rectifier.* 

The  light  of  the  Cooper-Hewitt  lamp  is  intensely  green  and 
it  is  entirely  unsatisfactory  where  objects  must  be  seen  in  their 
natural  colors  as  by  day-light.  When  color  values  are  not 
important,  for  example  in  shops  and  draughting  rooms,  the 
lamp  is  quite  satisfactory. 

The  Quartz  lamp  is  a  mercury-vapor  lamp,  with  a  containing 
tube  made  of  fused  silica  or  quartz.  It  differs  from  the  Cooper- 
Hewitt  lamp  in  that  a  greater  amount  of  energy  can  be  delivered 
to  a  small  tube.  The  tube  becomes  red-hot  during  the  opera- 
tion of  the  lamp  and  the  enclosed  vapor  gives  an  extremely  bril- 
liant light.  The  light  from  the  quartz  lamp  contains  a  small 
amount  of  red,  and  the  light  is  therefore  of  a  more  pleasing 
quality  than  the  light  of  the  Cooper-Hewitt  lamp. 

70.  The  glow  lamp. — The  most  extensively  used  type  of 
electric  lamp  is  the  familiar  incandescent  lamp  or  glow  lampt 
in  which  a  fine  filament  of  carbon  or  metal  is  heated  to  incan- 
descence by  the  electric  current.  The  filament  is  enclosed  in 
a  glass  bulb  from  which  the  air  is  exhausted,  the  object  being 
to  protect  the  filament  from  the  oxygen  of  the  air  and  to  elim- 

*  See  Dynamos  and  Motors,  Chapter  XIII. 


134  ELECTRIC    LIGHTING. 

inate  the  great  cooling  effect  which  exists  when  the  filament  is 
surrounded  by  gas  of  any  kind. 

There  are  five  important  kinds  of  glow  lamps  as  follows: 

(a)  The  old  style  carbon-filament  lamp. 

(b)  The  "metalized"  carbon-filament  lamp  which  differs  from 
the  old  style  in  that  the  carbon  filament  is  heated  to  an  extremely 
high  temperature  in  an  electric  furnace  before  it  is  mounted 
in   the   lamp. 

(c)  The  tantalum  lamp  in  which  the  filament  is  a  fine  wire  of 
metallic  tantalum. 

(d)  The  tungsten  lamp  in  which  the  filament  is  a  fine  wire  of 
metallic  tungsten.     The  tungsten  lamp  is  sometimes  called  the 
mazda    lamp. 

(e)  The  Nernst  lamp  in  which  the  glower  is  a  small  rod  of 
porcelain-like   material.* 

The  carbon-filament  lamp  (old  style  and  metalized)  and  the 
tungsten  lamp  are  by  far  the  most  important. 

The  carbon-filament  lamp  stands  rough  handling  without 
breakage  of  the  filament  and  it  is  cheap;  but^it  is  not  very  effi- 
cient. The  tungsten  lamp  on  the  other  hand  is  more  fragile 

*  An  interesting  article  on  carbon-filament  lamp  manufacture  by  M.  K.  Eyre 
'£  given  in  The  Electrical  World,  pages  9-13,  January  5,  1895. 

The  "metalizing"  process  of  carbon-filament  manufacture  is  described  by  J.  W. 
Howell  in  the  Transactions  of  the  American  Institute  of  Electrical  Engineers,  Vol. 
XXIV,  pages  839-849,  June,  1905. 

A  discussion  of  the  tantalum-filament  glow  lamp  is  given  by  Bolton  and  Feuer- 
lein,  Electrotechnische  Zeitschrift,  Vol.  XXVI,  pages  105-108,  January,  1905. 

"  New  Types  of  Incandescent  Lamps,"  a  discussion  of  the  early  process  of 
tungsten  filament  manufacture  and  a  discussion  of  the  characteristics  of  metal 
filament  lamps,  by  C.  H.  Sharp,  Transactions  of  the  American  Institute  of  Electrical 
Engineers,  Vol.  XXV,  pages  815-864,  November,  1906. 

The  manufacture  of  malleable  tungsten  which  can  be  drawn  into  fine  wire  is 
described  by  W.  C.  Coolidge,  Transactions  of  the  American  Institute  of  Electrical 
Engineers,  Vol.  XXIX,  pages  961-965,  May,  1910. 

The  Nernst  lamp  is  described  by  A.  J.  Wurts  in  the  Transactions  of  the  American 
Institute  of  Electrical  Engineers,  Vol.  XVIII,  pages  545-58?.  1901. 

The  process  of  manufacture  of  the  Nernst  lamp  is  described  in  The  Electrical 
World  and  Engineer,  Vol.  XLIII,  pages  981-985,  May  21,  1904. 


LAMPS,   LAMP    SHADES    AND    REFLECTORS. 


COST  OF  LIGHTING  BY  GLOW  LAMPS 
(Energy  at  ip  cents  per  kilowatt-hour.) 

B 

•sju33  ni 

OOO'I  JOJ   S^AVOU 

•3"M"  dmBHT  DUB 

O\  O    10  O  OO  00  O 
t^*  o\  co  O  ^t~  ^sh  t^ 

*  The  words  cancf/e  and  candle-power  signify  mean  horizontal  candle-power. 
f  Prices  of  lamps  are  net  prices,  March,  1912,  on  $300  contract. 
Old  style  carbon  lamps  and  tantalum  lamps  are  practically  obsolete  and  they  are  therefore  omitted  from  this  table. 
Candle-hours  during  life  is  found  by  multiplying  initial  candle-power  by  hours  total  life  by  deterioration  factor. 
This  table  refers  to  what  is  called  "top  efficiency."  See  page  139. 

0 

•jnoq-HBM. 

-0[I}I  J3d  SJU33 

oi  JB  sanoq 

-31PUB3  OOO'I 

joj  AJ8J3U3  J° 
sju33  ui  jso3 

0    CO  t  0    0    0    0 
^"  t^*  ON  ^J"  ^t"  ^T  ON 

Os  to  w   oi   o*   o*   M 

. 

•SJU33  ui  sjnoq 

-3[pUB3000'I  JOJ 

\O  O    t**»  T}"  O\  O\  ^i 
CO  ^T  5-  S    S"  0  M 

oo 

ESS 

Illllli 

M  00    O  oo    O    O    O 

H     HI     CO    ^  00     M     M 

M     O] 

ts 

•sjnoq 
3u;jnQ  paums 

10  10  O    O    O    O    O 

co  c*<  "3*  ^o  o  10  10 

VO 

4/SJU33  m 

O\  O    10  10  O    10  O 

to  10  Tt  N  o\  co  t~ 

M  co  ^r  1000  cooo 

H     H 

„ 

IBJOJ,  SJHOJJ 

§000000 
o  o  o  o  o  o 

- 

_— 

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O    O\  «s    O   -^  t^  H 

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„ 

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O     M     CO  OO   OO   OO     CO 
IO    CO    N     HI     M     M     M 

• 

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> 

'.'.'.'.'.'.. 

a    

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J8  :  :  :  ; 

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9 

"^  c  cs  a  a  ti  c 
*j  c  c  c  c  c  c 

136  ELECTRIC   LIGHTING. 

and  it  is  more  expensive  than  the  carbon-filament  lamp,  but 
it  is  much  more  efficient. 

A  comparison  of  costs  of  carbon,  tantalum  and  tungsten 
lamps  is  shown  in  the  accompanying  table,  energy  cost  being  10 
cents  per  kilowatt-hour. 

It  is  not  strictly  correct  to  compare  a  carbon  lamp  with  a  tungsten  lamp  on  the 
basis  of  mean  horizontal  candle-power  as  is  done  in  this  table  because  the  mean 
spherical  candle-power  of  the  regular  type  of  carbon  lamp  is  about  0.85  of  its  mean 
horizontal  candle-power  whereas  the  mean  spherical  candle  power  of  a  regular 
type  of  tungsten  lamp  is  only  about  0.79  of  its  mean  horizontal  candle-power.  The 
correct  basis  of  comparison  is  the  total  amount  of  light  emitted;  to  reduce  the  values 
in  columns  9,  10  and  n  to  this  correct  basis  the  tungsten  costs  should  be  multiplied 
by  0.85/0.79. 

An  important  matter  which  is  shown  very  clearly  in  this 
table  is  that  more  than  nine-tenths  of  the  cost  of  lighting  by  glow 
lamps  is  for  energy,  and  less  than  one-tenth  of  the  cost  is  for  lamp 
renewals.  The  users  of  electric  light  hesitate,  however,  to  pur- 
chase a  high-priced  tungsten  lamp  when  they  can  get  a  low- 
priced  carbon  lamp  or  when  their  contract  with  the  lighting 
company  calls  for  free  renewals  of  their  carbon  lamps.  This 
is  a  very  short-sighted  policy  because  the  higher-priced  tungsten 
lamp  has  a  longer  life  than  the  carbon  lamp  and  this  longer 
life  alone  makes  up  for  a  large  part  of  the  greater  cost,  but 
especially  because  the  saving  in  energy-cost  which  can  be 
realized  by  the  high-priced  tungsten  lamp  may  be  ten  or  twenty 
times  the  cost  of  the  lamp. 

A  given  glow  lamp  is  usually  rated  by  the  manufacturers 
for  a  specified  supply  voltage  as  explained  below,  but  the  lamp 
can,  of  course,  be  o  erated  at  a  higher  or  lower  voltage.  The 
effect  of  a  higher  voltage  is  to  give  a  greatly  increased  candle- 
power,  an  increased  power  consumption  (watts),  a  decreased 
watts-per-candle,  and  a  shortened  life.  A  low  power  consump- 
tion in  watts  per  candle  is,  of  course,  desirable  because  it  saves 
in  the  cost  of  energy,  but  a  short  life  is  undesirable  because 
short  life  involves  high  renewal  cost.  It  is  therefore  important 
to  make  a  proper  compromise  between  these  two  items  of  cost 


LAMPS,   LAMP   SHADES   AND    REFLECTORS. 


137 


so  as  to  obtain  a  minimum  total  cost.  This  matter  is  shown 
by  the  curves  in  Fig.  88.  The  pairs  of  curves  At  B,  Ct  D  and 
E  refer  to  energy  c^osts 
of  2,4,  6,  8  and  10  cents 
per  kilowatt-hour  re- 
spectively. These  curves 
refer  to  an  8o-candle- 
power  tungsten  lamp. 
The  abscissas  represent 
watts  per  candle,  and 
the  ordinates  -represent 
the  costs  for  1 ,000  hours' 
use  of  an  8o-candle-power 
lamp  of  the  following 
items:  (a)  energy  cost, 
(b)  renewal  cost,  and  (c) 
total  cost.  The  wavy 
line  connects  the  mini- 
mum points  of  the  total 
cost  curves.  Thus  when 
energy  costs  i  o  cents  per 
kilowatt-hour  a  tungsten 
lamp  of  the  size  specified 
gives  light  at  a  minimum 
total  cost  when  operated 
so  as  to  consume  about 
I.I  watts  per  mean  horizontal  candle-power. 

The  cost  of  energy  per  kilowatt-hour  in  a  large  manufacturing 
plant  is  usually  less  than  two  cents  and  sometimes  less  than  one 
cent.  It  is  therefore  important  to  consider  total  costs  of  lighting 
by  glow  lamps  (lamp  renewal  cost  plus  energy  cost)  when  the 
rate  per  kilowatt-hour  is  less  than  2  cents.  These  costs  are 
shown  by  the  ordinates  of  the  curves  in  Fig.  89.  These  curves 
show  that  the  tungsten  lamp  is  cheaper  than  the  carbon-filament 
lamp  down  to  an  energy  rate  of  about  0.2  cent  per  kilowatt-hour. 


1.2  __, 

watts  per  candle 

Fig.  88. 


138 


ELECTRIC   LIGHTING. 


The  carbon-filament  lamp  is  properly  used  where  it  is  sub- 
jected to  rough  handling  or  where  it  is  used  only  a  very  small 
portion  of  the  time.  Thus  the  drop-lamp  which  a  machinist 
uses  about  a  lathe  or  boring-mill  and  the  lamps  one  uses  in  a 
cellar  or  closet  should  be  carbon-filament  lamps. 


rate  per  kilowat-hour  in  cents 


Glow  lamp  ratings* — To  rate  a  thing  like  a  glow  lamp  is  to 
specify  the  conditions  under  which  it  is  to  be  used,  and  the 
results  to  be  obtained  by  its  use.  Manufacturers  usually  rate 
a  glow  lamp  in  terms  of  the  voltage  for  which  the  lamp  is  to  be 
used.  Thus  a  no- volt  lamp  is  one  that  is  designed  to  operate 
from  no-volt  mains.  In  addition  to  its  voltage  rating,  it  is 
necessary  to  specify  the  approximate  candle-power  of  the  lamp 

*  See  Circular  No.  13  of  the  U.  S.  Bureau  of  Staudards  for  standard  specifications 
for  the  purchase  of  incandescent  electric  lamps. 

The  Electrical  Testing  Laboratories,  8oth  Street  and  East  End  Avenue,  N.  V. 
City,  have  unsurpassed  facilities  for  testing  lamps  for  purchasers. 


LAMPS,   LAMP   SHADES  AND    REFLECTORS. 


139 


or  to  specify  the  approximate  power  consumption  of  the  lamp 
in  watts  at  its  rated  voltage.  Carbon-filament  lamps  are  usually 
rated  in  candle-powe/,*  and  tungsten  lamps  are  usually  rated 
in  terms  of  their  power  consumption.  Thus  we  speak  of  a 
i6-candle-power  carbon-filament  lamp  or  of  a  loo-watt  tungsten 
lamp. 

The  three-efficiency  scheme  of  rating  tungsten  lamps. — From  Fig. 
88  it  is  evident  that  it  is  sometimes  economical  to  burn  tungsten 
lamps  at  low  watts-per-candle  and  sometimes  economical  to 
burn  tungsten  lamps  at  high  watts-per-candle.  Therefore,  manu- 
facturers offer  the  purchaser  a  choice  of  watts-per-candle  in  lamps 
of  any  given  voltage  and  power  rating.  Three  efficiencies  are 
offered  in  regular  lamps;  namely,  "top  efficiency,"  "middle 
efficiency"  and  "bottom  efficiency"  as  shown  in  the  following 
table.  If  a  lamp  user  pays  a  high  rate  per  kilowatt-hour  for  his 
energy,  he  should  order  "top  efficiency"  lamps,  and  if  he  pays  a 
low  rate  per  kilowatt-hour  for  his  energy,  he  should  order  "bot- 
tom efficiency"  lamps. 


LIFE  AND  EFFICIENCY  TABLE  FOR  REGULAR  TUNGSTEN  LAMPS' 


Size  of 

Top  Efficiency. 

Middle  Efficiency. 

Bottom  Efficiency. 

Lamp  in 
Watts. 

Watts  per 
Candle.* 

Life  in 
Hours. 

Watts  per 
Candle. 

Life  in 
Hours. 

Watts  per 
Candle. 

Life  in 
Hours. 

25 

I-3I 

,OOO 

1-37 

,300 

•43 

,7OO 

40 

1.23 

,OOO 

1.28 

,3OO 

•33 

,70O 

60 

I.I8 

,OOO 

1.23 

,300 

.28 

,7OO 

IOO 

I.I8 

,000 

1.23 

,300 

.28 

,7OO 

150 

1.18 

,000 

1.23 

,300 

.28 

,7OO 

250 

1.  13 

,OOO 

1.18 

,300 

•23 

,700 

Candle-power  ratings  of  glow  lamps. — It  is  the  universal  practice 
to  rate  a  glow  lamp  by  giving  its  mean  hori  ?0ntal  candle-power. 

*Mean  horizontal  candle-power. 


140 


ELECTRIC   LIGHTING. 


The  mean  horizontal  candle-power,  however,  is  not  an  exact 
measure  of  the  amount  of  light  emitted  by  a  lamp ;  the  amount  of 
light  emitted  must  be  expressed  in  spherical-candles  or  in  lumens. 
The  factor  by  which  the  mean  horizontal  candle-power  of  a  lamp 
must  be  multiplied  to  give  its  mean  spherical  candle-power  is 
called  the  spherical  reduction  factor  of  the  lamp.  The  spherical 
reduction  factor  of  the  regular  carbon-filament  lamp  is  about 
0.85,  and  the  spherical  reduction  factor  of  the  regular  tungsten 
lamp  is  about  0.79.  To  reduce  mean  spherical  candle-power  to 
lumens  multiply  by  471-. 

Variations  of  candle-power  and  watts  due  to  variation  of  voltage. 
— Glow  lamps  are  generally  supplied  with  current  from  "constant 
voltage"  mains,  but  the  supply  voltage  always  varies  irregularly 


irtn 

/ 

/ 
/ 

;/ 

/ 

/ 

// 

140 

120 
IOO 
80 
60 

c/ 

/  . 
/ 

/, 
/  f 

'TU 

C.* 

l^ 

z 

// 

'/ 

1 

/ 

y// 

K. 

Ta 

I 

/ 

<//: 

y 

- 

=3 

# 

/ 

8 

A 

1 

S 

g 

* 

s 

S 

'/ 

To 

-^ 

s* 

f 

Tu. 

^ 

s'/ 

X 

,>• 

•^x 

'  / 

r 

-c. 

M. 

^ 

/ 

' 

oer 

cen 

t    V 

Oltf 

88         9a        96         100        104        108       112        u 
Fig.  90. 

through  a  range  of  one  or  two  per  cent,  (indeed  the  variation  of 
voltage  is  much  more  than  one  or  two  per  cent,  when  a  central 
station  is  poorly  designed  or  carelessly  operaced),  and  all  of  the 
connected  lamps  fluctuate  in  candle-power  as  the  supply  voltage 
rises  and  falls.  This  fluctuation  of  candle-power  is  very  un- 
pleasant, and  metal-rilament  glow  lamps  have  an  advantage  over 


LAMPS,   LAMP   SHADES   AND    REFLECTORS. 


carbon-filament  lamps  in  that  the  variation  of  candle-power  due 
to  a  given  variation  of  voltage  is  less  for  metal-filament  lamps 
than  for  carbon-filament  lamps.  The  ordinates  of  the  curves 
in  Figs.  90  and  91  show  candle-powers  and  watts  for  various 


Ta 


Tu 


-CM. 


percent  volt 


C.M 


Ta 


Tu 


92  90 


Fig.  91. 


values  of  voltage  (abscissas).  The  normal  value  of  each  item 
(voltage,  candle-power  and  watts)  is  taken  as  100  so  that  the 
departures  from  the  normal  values  may  be  read  off  directly  in 
per  cent.  Thus  a  two  per  cent,  increase  of  voltage  (100  to  102 
in  Fig.  90)  causes  a  12  per  cent,  increase  of  candle-power  of  an 
old  style  carbon-filament  lamp  (curve  C),  a  10  per  cent,  increase 
of  candle-power  of  a  metalized  carbon-filament  lamp  (curve  CM  )  . 
and  a  7  per  cent,  increase  of  candle-power  of  a  tungsten  lamp 
(curve  Tu)  . 

Slow  deterioration  of  glow  lamps  in  service.  —  A  glow-lamp  fila- 
ment is  always  operated  at  a  temperature  which  causes  a  slow 
change  of  the  filament  and  an  ultimate  deterioration  of  the  lamp. 
This  deterioration  is  chiefly  of  two  kinds,  namely,  (a)  an  increase 
of  resistance  of  the  filament  which  causes  a  decrease  of  power 
consumption  and  a  very  considerable  decrease  of  candle-power, 
and  (b)  a  blackening  of  the  lamp  bulb  which  involves  a  very 
great  loss  of  light.  If  a  lamp  is  used  long  enough  the  filament  is 
weakened  until  it  breaks. 

It  is  usually  advisable  to  use  a  tungsten  lamp  until  the  filament 


142 


ELECTRIC    LIGHTING. 


breaks.  Occasionally,  however,  the  bulb  of  a  tungsten  lamp 
blackens  and  such  a  lamp  should  be  discarded  when  the  blacken- 
ing causes  a  serious  loss  of  light. 

A  carbon-filament  lamp  should,  as  a  rule,  not  be  used  until 
the  filament  breaks,  it  is  cheaper  to  throw  away  an  old  carbon- 
filament  lamp  and  buy  a  new  one  than  it  is  to  use  the  old  lamp 
at  a  greatly  decreased  efficiency  (increased  watts-per-candle) . 
A  carbon-filament  glow  lamp  is  usually  considered  to  have  reached 
the  end  of  its  useful  life  when  its  candle-power  falls  to  80  per 
cent,  of  its  initial  value. 

The  curves  in  Fig.  92*  show  the  change  of  candle-power  of 
various  kinds  of  glow  lamps  with  age;    C,    CM,   Ta   and    Tu 


1  14° 

P- 
—  f- 

\  r 
\J 

'a 

^  — 

\ 

\ 

c  I0° 
e,  80 

N 

. 

1  — 

Tut 

r^ 

^ 

V 

^ 

—  - 

^ 

. 

T^ 

^_^ 

•  . 

— 

— 

— 

-—- 

— 

—  - 

—  —  . 

L'. 

M. 

"~^-» 

-  ^ 

^ 

--- 

_^_ 

3          3           4           56           789 

Jiundreds  of  hours 
Fig.  92. 

refer  to  carbon,  "metalized"  carbon,  tantulum  and  tungsten, 
respectively. 

In  estimating  the  cost  of  lighting  it  is  important  to  estimate 
the  illuminating  power  of  a  lamp  on  the  basis  of  its  average 
candle-power  during  its  life.  Thus  the  average  candle-power  of  a 
tungsten  lamp  during  its  life  is  from  0.90  to  0.95  of  its  candle- 
power  when  new.  See  page  149. 

Regular  lamps  and  special  lamps. — Great  numbers  of  glow 
lamps  are  used,  in  the   ordinary  constant-voltage   system,  for 

*  These  curves  are  taken  from  Wickenden's  Illumination  and  Photometry' 
The  tungsten  lamp  curve  refers,  apparently,  to  an  old-style  tungsten  lamp.  More 
recent  deterioration  curves,  and  a  discussion  of  the  important  subject  of  deterio- 
ration are  given  by  Sydney  W.  Ashe,  Transactions  of  the  Illuminating  Engineering 
Society,  Vol.  VI,  pages  503-570,  June,  1911. 


LAMPS,   LAMP   SHADES    AND    REFLECTORS. 


143 


lighting  houses  of  all  kinds,  and  these  lamps  are  made  of  standard 
form  so  as  to  fit  standard  forms  of  sockets  and  shades.  Such 
lamps  are  called  regular  lamps.  Glow  lamps  for  street  lighting, 
sign  lighting,  and  car  lighting,  are  called  special 
lamps.  Very  small  lamps  for  batteries  are  called 
miniature  lamps. 

Figure  93  shows  the  special  form  of  tungsten 
lamp  which  is  used  when  a  large  number  of  lamps 
are  connected  in  series  for  street  lighting.  These 
lamps  have  a  heavy  filament  (low  voltage)  and  they 
are  made  in  a  variety  of  sizes,  from  25  to  350  candle- 
power  with  current  ratings*  from  3.50  to  7.5  amperes. 

71.  Comparison  of  electric  lamps. — An  important  matter  in 
connection  with  a  lamp  is  the  distribution  of  light  around  the 
lamp.  Thus  the  candle-power  distribution  curves  of  carbon- 
filament  and  tungsten-filament  glow  lamps  with  and  without 


Fig.  93. 


Fig.  94  a. 

shades  are  shown  in  Figs.  64,  65  and  71.  Candle-power  dis- 
tribution curves  of  the  more  important  types  of  arc  lamps  are 
shown  in  Figs.  94  a  and  94  b.  The  numbers  of  the  curves  corre- 
spond to  the  serial  numbers  in  the  following  tables. f  Curve  4 
in  Figs.  94  a  and  94  b  refers  to  the  same  lamp,  namely,  the  6.6 
ampere  magnetite-arc  lamp  equipped  with  an  enamel  reflector, 

*  Series  tungsten  lamps  are  rated  on  the  basis  of  current  and  candle-power 
(mean  horizontal  candle-power). 

t  Candle-power  distribution  curves  of  mercury-vapor  lamps  are  given  by  Sydney 
W.  Ashe,  Transactions  of  the  Illuminating  Engineering  Society,  Vol.  VI,  pages 
5I3-SI6,  June,  1911. 


144 


ELECTRIC   LIGHTING. 


as  furnished  by  General  Electric  and  Westinghouse  Companies 
for  street  lighting. 

In  laying  out  the  lighting  plans  of  a  shop  or  factory  one  needs 
to  consider  the  intensity  of  illumination  on  the  working  plane  as 
explained  in  Art.  81.  The  following  table*  gives  the  values  of 


Fig.  94  6. 

Ih  (horizontal  illumination)  produced  by  various  arc  lamps. 
The  height  of  the  lamp  above  the  working  plane  is  in  each  case 
assumed  to  be  50  feet,  and  x  is  the  horizontal  distance  from  the 
lamp  to  the  point  on  the  working  plane  where  Ih  is  reckoned. 

By  making  use  of  the  law  of  inverse  squares  (Art.  48)  it  is 
easy  to  use  this  table  to  find  the  intensity  of  illumination  (hori- 
zontal) at  a  point  at  any  given  distance  d  horizontally  from  any 
one  of  the  lamps  placed  at  any  given  height  H  above  the  working 
plane.  The  rule  is  as  follows:  Find  from  the  table  the  value  of  Ih 
for  the  lamp  50  feet  high,  and  for  x  =  d  X  5o/#>  and  multiply  the 
value  of  Ih  so  found  by  (so/  H)2. 

*  This  table  was  calculated  from  the  candle-power  curves  of  Figs.  940  and  946, 
using  equation  (166). 


LAMPS,   LAMP   SHADES   AND    REFLECTORS. 


145 


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146  ELECTRIC   LIGHTING. 

Example. — To  find  the  horizontal  illumination  at  a  point  80 
feet  from  an  inclined-carbon  flame-arc  lamp  40  feet  above  the 
working  plane.  Multiply  80  by  50/40,  giving  x  =  100  feet. 
The  value  of  IH  in  the  table  corresponding  to  this  value  of  x 
is  0.102,  which,  multiplied  by  (50/40)2  gives  the  desired  result, 
namely,  0.127  foot-candle. 

To  find  the  distance  d  from  a  lamp  H  feet  above  the  working 
plane  to  give  a  prescribed  horizontal  illumination,  multiply  the 
prescribed  horizontal  illumination  by  (H/5o)2  to  get  IH  as  per 
table,  find  the  corresponding  value  of  x  from  the  table  and  multiply 
this  value  of  x  by  ( Hl$o)  to  get  the  desired  value  of  d. 

Example. — To  find  d  for  which  a  6.6-ampere  magnetite-arc 
lamp  hung  30  feet  high  will  give  0.5  foot-candle  horizontal 
illumination;  the  value  of  (H/^o)2  X  0.5  is  0.18  foot-candle, 
and  the  corresponding  value  of  x  is  50  feet,  so  that  the  desired 
value  of  d  is  30  feet. 

Comparative  costs. — The  following  table*  shows  the  approxi- 
mate cost  of  producing  100,000  downward  lumens  6  hours  per 
day  300  days  per  year  using  different  kinds  gf  lamps.  It  must 
be  remembered  that  this  table  refers  to  averagef  conditions,  and 
to  interpret  the  table  properly  the  following  matters  must  be 
taken  into  consideration. 

(a)  Multiple  arc  lamps  and  series  arc  lamps. — When  few  arc 
lamps  are  to  be  installed,  it  is  always  most  convenient  to  supply 
them  from  existing  constant-voltage  mains.  Each  lamp  is  pro- 
vided with  a  ballast,  as  explained  on  page  128,  and  the  lamps  are 
connected  singly  J  across  the  constant  voltage  mains.  Lamps 
designed  to  be  connected  in  this  way  are  called  multiple  lamps. 

When  many  arc  lamps  are  to  be  installed,  they  may  be  con- 

*  This  table  has  been  prepared  from  data  collected  from  various  sources.  A 
discussion  of  costs  of  street  lamps  is  given  in  Bulletin  No.  51  of  the  Illinois  Engineer- 
ing Experiment  Station  by  J.  M.  Bryant  and  H.  G.  Hake,  on  Street  Lighting. 

f  See  statement  concerning  averages  on  page  2. 

J  Sometimes  two  lamps  are  connected  in  series.  In  case  of  a  5oo-volt  supply 
six  or  seven  lamps  can  be  connected  in  series.  Lamps  designed  to  be  connected  in 
this  way  are  called  series-multiple  lamps. 


LAMPS,   LAMP   SHADES    AND    REFLECTORS. 


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LAMPS,   LAMP   SHADES   AND    REFLECTORS.  149 

nected  in  series  to  a  constant-current  supply  (see  Art.  87).  This 
arrangement  reduces  the  cost  of  wiring  to  a  minimum  and  it 
eliminates  the  wasteof  energy  in  lamp  ballasts.  Lamps  designed 
to  be  connected  in  this  way  are  called  series  lamps. 

A  multiple  lamp  is  rated  by  specifying  the  voltage  of  supply 
for  which  the  lamp  is  designed  and  the  current  which  the  lamp 
will  take  when  it  is  properly  adjusted.  A  series  lamp  is  rated 
by  specifying  the  current  for  which  the  lamp  is  designed. 

All  of  the  arc  lamps  referred  to  in  the  table  are  series  lamps. 
Nearly  every  type  of  arc  lamp,  however,  is  offered  for  sale  either 
as  a  series  lamp  or  as  a  multiple  lamp;  a  multiple  lamp  uses 
about  1.4  times  as  much  power  as  a  series  lamp  when  the  same 
amount  of  power  is  expended  at  the  arc. 

(b)  Cost  of  energy.* — As  a  rule  series  lamps  are  used  under 
conditions  which  involve  low  cost  of  energy  (long  hours  of  service 
and  large  demand  for  power),  whereas  multiple  lamps  are,  as  a 
rule,  used  under  conditions  which  involve  high  cost  of  energy  (short 
hours  of  service  and  small  demand  for  power) .     Thus  a  company 
might  furnish  power  for  operating  the  street  lamps  of  a  city 
(about  4,000  hours  of  service  per  year)  at  2  or  3  cents  per  kilowatt- 
hour,  and  be  fully  justified  in  charging  8  or  10  cents  per  kilowatt- 
hour  for  power  for  operating  two  or  three  arc  lamps  in  a  store 
(about  i  ,000  hours  service  per  year) . 

(c)  Deterioration  factor. — The  number  of  lamps  in  column  3  is 
reckoned  on  the  basis  of  initial  candle-power,  whereas  a  fair  com- 
parison of  costs  must  be  based  upon  average  candle-power  during 
the  life  of  a  lamp.     The  ratio,  average  candle-power  during  the 
life  of  a  lamp  divided  by  the  initial  candle-power  of  the  lamp,  is 
called  the  deterioration  factor  of  the  lamp.     The  annual  costs  in 
column  14  should  be  divided  by  the  deterioration  factors.     The 
values  of  this  factor  are  as  follows: 

*  See  Art.  87,  page  183. 


150 


ELECTRIC   LIGHTING. 
TABLE  OF  DETERIORATION  FACTORS* 


Tungsten. 

Carbon-arc. 

Magnetite-arc. 

Enclosed  Flame- 
arc. 

Cooper-Hewitt. 

0.90  to  0.95 

0.80  to  0.85 

0.90 

0.85 

0.65  to  0.75 

(d)  A   given  number  of  downward  lumens  does  not  mean  the 
possibility  of  illuminating  a  certain  floor  area. — Thus  the  light 
from  a  few  very  high  candle-power  lamps  cannot  be  satisfactorily 
distributed  over  a  large  floor  space  unless  the  lamps  are  placed 
at  a  sufficient  height  overhead  and  unless  the  space  is  free 
from  obstructions  such    as  beams  and  belts  and  shafting  (see 
Art.  78).     It  is  misleading  to  compare  the  costs  of  small  lamps  and 
large  lamps  on  the  basis  of  quantity  of  light. 

Moderately  small  tungsten  lamps  give  the  cheapest  satisfactory 
illumination  when  the  height  of  the  lamps  is  limited  to  12  or  15 
feet  or  where  there  are  many  obstructions.  On  the  other  hand 
quartz  tube  lamps  are  only  suitable  for  illuminating  large  open 
spaces  where  the  lamps  can  be  placed  40  or  50  feet  high.  Be- 
tween these  two  extremes  there  is  a  wide  field  of  usefulness  for 
high  candle-power  tungsten  lamps,  for  Cooper-Hewitt  lamps  and 
for  magnetite-arc  and  flame-arc  lamps. 

(e)  Maintenance. — The  maintenance  cost  as  given  in  column 
10  includes  in  every  case  the  cost  of  regular  inspection,  the  cost 
of  cleaning  globes  and  reflectors,  the  cost  of  material  and  labor 
for  renewal  of  parts  which  wear  outf  or  are  occasionally  broken, 
and  the  cost  of   material  and   labor  for   repairing  lamp  mech- 
anisms. 

The  maintenance  cost  varies  greatly:  (a)  because  different 
kinds  of  service  differ  greatly  in  the  required  frequency  of  cleaning 

*  These  results  are  based  upon  very  few  observations,  and  they  are  therefore 
not  to  be  depended  upon.  This  is  especially  true  in  view  of  the  fact  that  fre- 
quency of  cleaning  of  globes  and  reflectors  has  a  very  great  deal  to  do  with 
deterioration. 

t  Such  as  tungsten  lamps,  arc  lamp  electrodes,  Cooper-Hewitt  vapor  tubes, 
globes,  etc. 


LAMPS,   LAMP   SHADES   AND    REFLECTORS.  151 

of  globes  and  reflectors  and  in  the  amount  of  breakage,  (b)  because 
in  some  cases  the  lamps  are  difficult  of  access  and  the  cost  of 
trimming  and  cleaning  is  excessive,  and  (c)  because  the  main- 
tenance labor  can  be  more  efficiently  organized  when  a  great  many 
lamps  of  a  kind  are  to  be  cared  for  than  when  the  number  of 
lamps  is  small. 

The  maintenance  cost  in  the  table  refers  to  two  or  three  or  four 
thousand  hours  use  per  year.  When  lamps  are  used  only  a  few 
hundred  hours  per  year  the  maintenance  is  more  expensive  per 
hour. 

(f)  Color. — When  whiteness  of  light  is  a  necessity,  it  is  of 
course  meaningless  to  compare  the  cost  of  carbon-arc  lamps  and 
tungsten  lamps  with  the  cost  of  flame-arc  lamps  and  mercury- 
vapor  lamps.  See  Art.  76. 

72.  Lamp  globes,  shades  and  reflectors.* — Let  one  consider 
the  lamps  which  one  sees  everywhere,  on  city  streets,  in  stores 
and  public  halls,  and  in  residences,  and  one  will  realize  that  lamps 
are  almost  universally  equipped  with  shades  and  reflectors. 
These  shades  and  reflectors  are  used  for  three  distinct  purposes, 
namely,  (a)  to  eliminate  glare, f  (b)  to  throw  the  light  in  a  desired 
direction,  and  (c)  for  decoration. 

The  use  of  a  shade  for  the  elimination  of  glare  is  exemplified 
by  the  opal  and  ground  glass  globes  which  enclose  indoor  arc 
lamps  and  Welsbach  gas  lamps,  and  the  use  of  a  shade  for 
throwing  the  light  of  a  lamp  in  a  desired  direction  is  exemplified 
by  the  canopy  reflectors  commonly  used  on  street  lamps. 

In  most  cases  shades  and  reflectors  are  used  for  the  double 
purpose  of  eliminating  glare  and  directing  the  light  from  a  lamp. 

*See  Cravath  and  Lansingh,  Practical  Illumination,  pages  25-135,  McGraw 
Publishing  Company,  1907. 

The  results  of  an  extensive  series  of  experimental  studies  of  globes  and  reflectors 
by  R.  B.  Williamson  and  J.  H.  Klinck  are  given  in  Journal  of  Franklin  Institute, 
Vol.  CXLIX,  page  66,  1900. 

Also  see  papers  by  V.  R.  Lansingh,  Transactions  of  Illuminating  Engineering 
Society,  Vol.  II,  pages  37i~399.  and  Vol.  V,  pages  49-74. 

fSee  Art.  77- 


152  ELECTRIC   LIGHTING. 

Thus  the  shades  which  are  used  on  desk  lamps  eliminate  glare 
by  hiding  the  lamp  itself  from  view,  and  they  throw  the  light 
downwards  upon  the  desk. 

Lamp  shades  for  indoor  use  should  always  be  to  some  extent 
decorative.  Decorative  effects  are,  indeed,  the  primary  con- 
sideration in  the  elaborate  and  deeply  colored  shades  which  are 
frequently  used  in  parlors,  and  these  shades  are  highly  effective 
in  the  elimination  of  glare;  but  if  a  shade  is  to  direct  the  light  of 
a  lamp  where  it  is  needed,  the  shade  must  not  depart  very  widely 
in  shape  from  a  simple  cone  or  bowl ;  and  if  excessive  loss  of  light 
by  absorption  is  to  be  avoided,  the  shade  must  not  have  colored 
parts  which  are  intended  to  transmit  light. 

73.  Extensive,  intensive  and  focusing  shades. — Lamp  shades 
which  are  not  primarily  decorative  may  be  classified  according  to 
their  directing  action  on  the  light  of  a  lamp.  Thus  we  have  the 
focusing  shade  which  throws  the  light  downwards  in  a  very  intense 
narrow  beam,  the  intensive  shade  which  throws  the  light  down- 
wards in  a  fairly  narrow  beam  of  moderate  intensity,  and  the 
extensive  shade  which  throws  the  light  downwards  in  a  wide  beam. 
Thus  curve  B  of  Fig.  64  shows  the  distribution  of  candle-power* 
around  a  bare  tungsten  lamp,  curve  E  shows  the  distribution  of 
candle-power  when  the  lamp  is  equipped  with  a  typicalf  extensive 
reflector,  curve  I  shows  the  distribution  of  candle-power  when 
the  lamp  is  equipped  with  a  typical  intensive  reflector,  and  curve 
F  shows  the  distribution  of  candle-power  when  the  lamp  is 
equipped  with  a  typical  focusing  reflector. 

Extensive  shades  or  reflectors  are  the  most  generally  used. 
They  are  adapted  to  residence  lighting  where  small  rooms  with 
low  ceilings  are  the  rule.  Intensive  shades  are  suitable  for 
large  rooms  with  high  ceilings  where  the  lamps  are  distributed 

*  The  radius  vector  of  one  of  the  curves  in  Fig.  64  represents  the  candle-power 
in  that  direction,  and  therefore  it  is  strictly  correct  to  speak  of  the  curves  as  repre- 
senting the  distribution  of  candle-power.  Indeed  the  expression  distribution  of 
candle-power  is  better  than  the  more  general  expression  distribution  of  light. 

t  In  fact  curves  E,  I  and  F  refer  to  standard  line  prismatic  glass  reflectors  of 
the  Holophane  Company. 


LAMPS,   LAMP   SHADES   AND   REFLECTORS.  153 

uniformly  over  the  room.  Focusing  shades  are  used  for  rooms 
with  very  high  ceilings  and  for  producing  intense  local  illumina- 
tion on  a  desk  or  draughting  board  or  on  a  work  bench. 

To  classify  shades  according  to  their  directing  action  tends  to 
take  one's  attention  away  from  an  equally  important  matter,  the 
elimination  of  glare.  This  matter  is  best  considered,  however, 
in  the  following  description  of  particular  shades. 

74.  Metal  and  milk-glass  reflectors. — A  familiar  type  of  re- 
flector is  the  sheet  metal  cone,  which  is  made  deep  for  the  focusing 
type,  less  deep  for  the  intensive  type,  and  nearly  flat  for  the 
extensive  type.  In  the  cheaper  grades,  this  shade  is  made  of 
sheet  tin  painted  white  on  the  inside,  but  the  better  grades  are 
made  of  pressed  sheet  steel  with  white  porcelain  enamel  on  the 
inside.  Milk-glass  is  also  extensively  used  for  these  cone  re- 
flectors. 

When  lamps  which  are  used  for  illuminating  tables  and  desks, 
are  also  depended  upon  to  illuminate  the  upper  part  of  the  room, 
metal  reflectors  are  not  very  satisfactory,  especially  intensive 
and  focusing  types  of  metal  shades  are  not  satisfactory  under  the 
stated  conditions  because  metal  shades  allow  no  light  to  pass 
from  the  lamp  to  the  upper  part  of  the  room.  Milk-glass  cones 
are,  however,  quite  satisfactory  in  this  respect  as  are  also  the 
prismatic  reflectors  which  are  described  in  Art.  75. 

Porcelain  enamel  reflectors  are  used  very  extensively  in  street 
and  mill  lighting.  As  compared  with  prismatic  glass,  enamel 
reflectors  are  cheaper,  they  do  not  catch  and  hold  the  dust  as 
badly,  and  when  properly  made  they  throw  a  greater  portion 
of  the  light  of  a  lamp  downwards.  For  store  and  residence 
lighting,  however,  prismatic  glass  reflectors  are  more  extensively 
used  than  enamel  reflectors  for  reasons  above  stated  and  because 
prismatic  glass  is  more  decorative. 

When  the  shades  above  described  are  not  deep  enough  to  hide 
the  lamp  from  view,  the  lower  portion  of  the  lamp  bulb  should 
be  frosted*  to  reduce  the  glare  of  the  visible  portion  of  the  lamp 

*  Lamps  so  treated  are  said  to  be  bowl-frosted. 


154 


ELECTRIC    LIGHTING. 


filament.  This  is  quite  necessary  when  brilliant  tungsten  lamps 
are  used,  and  it  is  advisable  even  when  the  lamps  with  their  open 
shades  are  hung  near  the  ceiling  of  any  ordinary  room  because 
it  is  impossible  in  an  ordinary  room  to  place  a  lamp  entirely 
outside  of  the  field  of  vision. 

75.  The  prismatic  glass  reflector  is  a  cone  of  clear  glass  with 
vertical  prismatic  ribs  on  its  outside  surface.     Its  action  may  be 


inside 


outside 


Fig.  95. 


Fig.  96. 


Fig.  97. 


understood  from  Figs.  95,  96  and  97.  Any  ray  like  r,  Fig.  95, 
is  turned  backwards  (and  downwards)  by  total*  reflection, 
whereas  such  rays  as  5  and  t  pass  through  the  rounded  edges  of 
the  prisms  and  the  rounded  bottoms  of  the  intervening  grooves. 

*When  light  in  a  dense  medium  like  glass  strikes  the  surface  obliquely  it  is 
totally  reflected.  This  phenomenon  is  exemplified  by  the  brilliant  silvery  appear- 
ance of  the  surface  of  the  water  in  a  tumbler  when  the  surface  is  viewed  obliquely 
from  below. 


LAMPS,   LAMP   SHADES   AND    REFLECTORS. 


155 


Fig.  96  is  a  top  view  of  a  prismatic  reflector  showing  a  section 
of  the  reflector  along  the  plane  cd  in  Fig.  97.  The  small  circle 
at  the  center  in  Fig,  96  represents  the  lamp.  The  rays  of  light 
from  the  lamp  strike  the  faces  of  the  prismatic  ribs  very  obliquely 
and  are  totally  reflected  downwards  as  shown  in  Fig.  97. 

The  open  cone-shaped    prismatic  re- 
flectors are  not  usually  deep  enough  to 
completely  hide  the  lamp  from  view  and 
the   lamp   should    therefore    be    bowl-      ; 
frosted  to  reduce  the  glare. 

Another  type  of  prismatic  glass 
shade  has  horizontal  prismatic  ribs 
which  act  partly  by  refraction  and 
partly  by  reflection  as  shown  in  Fig. 
98  in  which  the  dotted  lines  represent 
rays  of  light  from  the  lamp.  The  faces 
ab  and  cd  are  refracting  faces  and 
the  faces  be  are  total  reflecting  faces.  This  type  of  prismatic 
lamp  shade  was  brought  out  in  England  in  1882  by  Mr. 
A.  P.  Trotter.*  It  is  now  manufactured  in  a  variety  of  rather 
ornamental  forms  by  the  HolopKane  Company.  These  orna- 
mental prismatic  shades  are  usually  made  in  the  form  of  com- 
plete spheres  which  enclose  the  lamp,  and  they  eliminate  glare 
almost  completely. 

*  A  very  interesting  account  of  the  development  of  this  shade  is  given  in  Trotter's 
Illumination,  pages  263-274,  Macmillan  and  Co.,  London,  191 1. 


Fig.  98. 


CHAPTER  VI. 

INTERIOR  ILLUMINATION. 

76.  The  illumination  of  a  room.* — A  room  may  be  said  to  be 
well  lighted  when  the  eye  is  easily  able  to  distinguish  the  various 
objects  in  the  room  in  minute  detail  of  perception.  This  com- 
pleteness of  visual  perception  depends  upon  three  conditions: 
namely,  (a)  a  sufficient  brightness  of  illumination,  (b)  a  proper 
location  of  the  light  sources  so  as  to  bring  out  that  combination 
of  soft  shadows  which  is  so  essential  to  the  perception  of  form, 
and  (c)  a  proper  composition!  of  the  light  so  as  to  bring  out 
those  physical  differences  in  objects  which  the  eye  perceives  as 
variations  of  color. 

(a)  The  necessity  of  having  a  sufficient  intensity  of  illumina- 
tion is,  of  course,  known  to  everyone.  The  ability  to  perceive 
fineness  of  detail  (called  visual  acuity)  depends  chiefly  upon 
intensity  of  illumination. 

Visual  acuity  is  always  measured  in  an  arbitrary  way,  for  example,  one  may 
measure  visual  acuity  as  the  distance  from  one's  eye  at  which  clear  black  print 
of  a  chosen  size  may  be  read,  and  the  dependence  of  visual  acuity  upon  intensity 

*  An  extremely  interesting  discussion  of  the  conditions  which  determine  visual 
perception  is  given  by  Helmholtz  in  his  popular  lecture  on  The  Relation  of  Optics 
to  Painting  which  is  translated  (by  E.  Atkinson)  in  the  second  series  of  Helmholtz's 
Popular  Lectures,  Longmans,  Green  &  Co.,  1903.  Everyone  who  is  concerned  with 
the  practical  problems  of  illumination  should  read  this  lecture.  Helmholtz's 
Popular  Lectures  are  published  in  German  under  the  title  Vortriige  und  Reden, 
2  volumes,  Braunschweig,  Vieweg  und  Sohn,  1884. 

Three  lectures  in  Helmholtz's  first  series  (translated  by  Dr.  Pye-Smith;  Long- 
mans, Green  &  Co.,  1873),  On  the  Theory  of  Vision,  also  have  a  bearing  upon  the 
important  practical  subject  of  illumination. 

See  also  the  lectures  by  Percy  W.  Cobb  and  by  Robt.  M.  Yerkes,  pages  525-604, 
Vol.  II,  Johns  Hopkins  University  Lectures  on  Illuminating  Engineering,  Baltimore, 
1911. 

t  The  composition  of  light  refers  to  the  relative  intensities  of  the  various  wave- 
lengths which  are  present  in  the  light. 

I56 


.    g, 

2     g 


INTERIOR    ILLUMINATION.  .  157 

of  illumination  may  be  determined  by  finding  the  distance  at  which  the  given 
type  can  be  read  for  different  intensities  of  illumination.  In  this  way  it  is  found 
that  visual  acuity  is  very  low  when  the  intensity  of  illumination  is  one  or  two 
tenths  of  a  foot-candle.  It  increases  rapidly  up  to  one  or  two  foot-candles  and 
then  it  increases  slowly  and  reaches  a  maximum  at  about  eight  or  ten  foot- 
candles. 

(b)  The  importance  of    the   second    condition    is   illustrated 
by  Figs.  99,  100  and  101,  which  show  a  face  illuminated  in  three 
different  ways.       In  Fig.  99  the  face    is  illuminated  by  light 
from  a  single  concentrated  source  (an  electric  arc),  without  any 
reflection  from  the  walls  of  the  room  to  soften  the  effect,  and  the 
shadows  are  extremely  harsh;  in  Fig.  100  the  face  is  illuminated 
by  light  from  a  broad  source  and  largely  from  one  side,  and  the 
shadows  are  soft;  in  Fig.  101  the  face  is  illuminated  by  light 
coming  equally  from  all  directions  and  there  are  no  shadows  at  all. 

A  room  may  be  sufficiently  illuminated  by  a  single  arc  lamp 
but  such  illumination  is  unsatisfactory,  even  when  the  eye  is 
shaded  from  the  direct  light  of  the  lamp,  because  the  excessive 
harshness  of  the  shadows  renders  the  perception  of  form  almost 
impossible.  The  light  from  a  single  brilliant  lamp  is  always 
softened,  however,  by  the  reflection  from  the  walls  and  ceiling 
of  a  room. 

The  vsecond  condition  is  not  important  where  purely  flat- 
surface  vision  is  required  as  in  a  draughting  room,  where  indeed 
it  is  important  to  eliminate  all  shadows  on  the  sheet  of  drawing 
paper. 

(c)  The  importance  of  the  third  condition  is  evident  when  one 
attempts  to  distinguish  delicate  colors  by  ordinary  lamp  light. 
Thus  the  light  of  an  ordinary  kerosene  lamp  is  very  deficient 
in  the  short  wave-lengths  (blue  and  violet),  and  a  deep  blue  or 
violet  piece  of  cloth  appears  almost  black  by  kerosene  lamp  light, 
False  color  values  are  produced  in  a  very  striking  way  by  the 
light  from  a  mercury- vapor  lamp  on  account  of  the  almost 
complete  absence  of  the  longer  wave-lengths  (red)  in  the  light 
from  this  lamp.     The  most  striking  illustration  of  false  color 
values,  however,  may  be  obtained  by  illuminating  a  batch  of 


158  .  ELECTRIC   LIGHTING. 

brilliantly  colored  worsteds  by  the  light  from  a  sodium  flame  in 
a  room  from  which  all  white  light  is  excluded.  All  differences  of 
tint  disappear  under  these  conditions,  and  a  given  piece  of 
worsted  merely  appears  to  be  light  or  dark  according  as  it  is  able 
or  unable  to  reflect  the  yellow  light  of  the  sodium  flame. 

The  carbon-arc  lamp  gives  a  nearer  approach  to  daylight  than 
any  other  commercial  form  of  lamp.*  The  whiteness  of  the  light 
from  the  carbon-arc  lamp  is  spoiled,  however,  by  the  excess  of 
violet  light  from  the  arc  stream  and  by  the  excess  of  red  and 
orange  light  from  the  moderately  heated  parts  of  the  carbons. 
These  defects  are  corrected  to  some  extent  in  the  intensified 
carbon-arc  lamp  which  burns  with  a  short  arc  thus  reducing  the 
violet  light,  and  small  carbons  are  used  thus  reducing  the  mod- 
erately heated  areas  near  the  ends  of  the  carbons. 

77.  Glare. — The  presence  of  excessively  brilliant  lamps  or 
excessively  brilliant  patches  of  light  in  a  field  of  vision  greatly 
hinders  visual  perception.  The  eye  adapts  itself  automatically 
to  the  brightest  lights  in  the  field  of  view,  and  all  perception  of 
detail  in  the  shadows  is  lost.  This  effect  is  called  glare,  and  it  is 
especially  marked  when  the  field  of  vision  includes  a  bright 
unshaded  lamp. 

The  explanation  of  glare  is  as  follows:  In  the  first  place  a 
beam  of  light  entering  the  eye  from  a  bright  source  illuminates 
the  whole  interior  of  the  eye  just  as  a  beam  of  sunlight  entering 
a  window  illuminates  a  room.  This  diffused  light  in  the  eye 
illuminates  and  excites  the  entire  retina,  including  those  portions 
where  the  images  of  the  deeper  shadows  fall,  and  thereby  tends 
to  obliterate  all  detail  of  perception.  In  the  second  place  the 
portions  of  the  retina  upon  which  the  brilliant  light  falls  become 
greatly  reduced  in  sensitiveness  by  fatigue,  the  continual  wander- 
ing of  the  eye  brings  the  image  of  a  dark  region  upon  this  fatigued 

*  The  Moore  vacuum-tube  lamp  (with  carbon  dioxide)  is  better  than  the  carbon- 
arc  lamp.  The  use  of  bluish  glass  for  absorbing  the  excess  of  red  and  yellow 
light  from  a  tungsten  or  carbon-arc  lamp  is  briefly  discussed  in  the  General  Electric 
Review  for  December  1911. 


INTERIOR    ILLUMINATION.  159 

portion  of  the  retina,  and  the  result  is  almost  total  blindness  like 
that  produced  when  one  looks  out  of  a  window  and  then  turns 
towards  a  dark  corner  of  a  room.  In  the  third  place  the  pupils 
of  the  eyes  contract  greatly  when  there  is  a  bright  light  in  the  field 
of  vision,  and  this  contraction  lessens  the  effective  brightness 
not  only  of  the  bright  portions  of  the  field,  but  also  of  the  deep 
shadows;  but  the  deep  shadows  are  already  insufficiently  illu- 
minated and  the  contraction  of  the  pupils  of  the  eyes  tends  to 
make  them  (the  shadows)  appear  like  black  patches  entirely 
devoid  of  detail. 

An  interesting  case  of  excessive  contrast  or  glare  is  that 
in  which  a  workman  at  a  loom,  for  example,  has  his  immediate 
work  illuminated  to  a  fair  degree  of  brightness  while  the  remainder 
of  the  room  is  left  in  darkness.  If  the  workman  could  keep  his 
eyes  upon  his  work  incessantly,  it  is  conceivable  that  this  kind 
of  illumination  might  be  satisfactory;  but  the  eye  moves  about 
in  spite  of  everything  one  can  do,  and,  under  the  assumed  condi- 
tions, the  workman  would  be  unable  to  see  when  he  glanced 
about  the  room  and  he  would  be  blinded  when  he  glanced  back 
at  his  work.  To  avoid  this  impracticable  situation  a  general 
illumination  of  the  room  is  necessary.  If  a  brilliant  light  is 
needed  upon  one's  work,  the  whole  room  must  be  fairly  well 
lighted,  and  the  necessary  local  illumination  must  be  produced 
in  addition  thereto. 

It  is  very  important,  in  arranging  for  the  illumination  of  a 
room,  to  place  the  lamps  outside  of  the  field  of  vision  if  possible, 
so  that  no  light  can  enter  the  eye  directly  from  the  lamps  and  render 
the  eye  insensible  to  the  delicate  shading  of  surrounding  objects. 
The  excessive  discomfort  that  is  produced  by  the  glare  of  im- 
properly located  lamps,  such,  for  example,  as  the  exposed  foot- 
lights of  a  poorly  arranged  stage,  is  due  not  only  to  the  physical 
pain  that  is  associated  with  long-continued  looking  at  a  bright 
light  but  more  especially  to  the  incessant  effort  of  trying  to  peer 
into  the  dark  region  beyond. 

When  a  lamp  cannot  be  removed  from  the  field  of  vision  the 


160  ELECTRIC   LIGHTING. 

bad  effects  of  glare  may  be  greatly  reduced  by  enlarging  the  lumin- 
ous surface  of  the  lamp  by  means  of  a  translucent  globe  or  shade. 

78.  Small  lamps  versus  large  lamps. — A  small  lamp,  as  the 
term  is  here  used,  is  a  lamp  which  gives  a  small  amount  of  light; 
and  a  large  lamp  is  a  lamp  which  gives  a  large  amount  of  light. 
A  given  amount  of  light  can  be  produced  more  cheaply  by  large 
lamps  than  by  small  lamps  because  large  lamps  are,  as  a  rule, 
more  efficient  (less  watts  per  lumen)  than  small  lamps  and  be- 
cause a  few  large  lamps  are  cheaper  to  install  and  cheaper  to 
maintain  than  many  small  lamps.     The  use  of  large  brilliant 
lamps  is,  however,  limited  by  two  conditions  as  follows: 

(a)  Satisfactory  distribution  of  light. — Whenever  it  is  necessary 
to  use  a  large  number  of  lamps  in  order  to  get  a  satisfactory 
distribution  of  light,  small  lamps  are  used  because  to  use  large 
lamps  would  give  an  unnecessarily  large  quantity  of  light.  It 
is  not  desirable,  however,  to  have  light  too  uniformly  distributed 
(by  using  a  great  number  of  small  lamps)  because  the  resulting 
illumination  is  flat,  that  is,  devoid  of  satisfactory  shadows. 

(6)  Elimination  of  glare. — A  large  lamp  an  one's  field  of  vision 
produces  a  much  more  unpleasant  glare  than  a  small  lamp,  and 
therefore  (even  if  a  proper  distribution  could  be  secured)  it  is 
not  advisable  to  use  large  lamps  in  rooms  with  low  ceilings  be- 
cause with  a  low  ceiling  a  lamp  cannot  be  placed  high  enough  to 
remove  it  entirely  from  one's  field  of  vision.  Large  lamps  must 
be  placed  high  overhead.  This  is  especially  true  of  lamps  which 
have  a  high  intrinsic  brilliancy;  such  lamps  must  not  be  placed 
in  the  field  of  vision  unless  they  are  shaded. 

When  the  indirect  system  of  lighting  is  employed,  however, 
very  large  brilliant  lamps  can  be  used  in  small  rooms. 

79.  The  indirect  system  of  lighting.* — A  favorite,  although 
somewhat  extravagant,  system  of  illumination  is  to  place  the 

*  A  good  discussion  of  indirect  lighting  is  given  by  L.  B.  Marks,  Johns  Hopkins 
University  Lectures  on  Ilhiminating  Engineering,  Vol.  II,  pages  691-702,  Baltimore, 
1911.  See  also  an  article  by  J.  R.  Cravath,  Transactions  of  the  Illuminating  En- 
gineering Society,  Vol.  IV,  pages  290-306,  1909. 


INTERIOR   ILLUMINATION. 


i6r 


famps  entirely  out  of  sight,  and  so  that  the  light  from  the  lamps 
may  fall  upon  the  ceiling  of  the  room.  Thus  Fig.  102  shows  the 
essential  features  of  such  an  arrangement.  The  lamps  are  placed 


ceiling 


wall 


Fig.  102. 


in  a  cove  within  a  few  feet  of 
the  ceiling  and  are  hidden  from 
view  by  a  high  moulding  as  in- 
dicated in  the  figure. 

The  indirect  system  of  illum- 
ination gives  an  extremely 
diffused  light  which  is  itself 
beautiful  and  pleasing,  but  it 
does  not  give  the  shadows 
which  are  essential  for  the  vis- 
ual perception  of  form.  This 
system  is  satisfactory  for  auditoriums  and  draughting  rooms, 
but  it  is  not  satisfactory  where  the  perception  of  form  is  of  great 
importance.  It  should  never  be  used  where  the  walls  and  ceiling 
are  liable  to  become  even  slightly  discolored  by  dust  or  smoke. 
A  modification  of  the  indirect  system  of  lighting  is  to  place 
arc  lamps  or  verv  high-candle-power  tungsten  lamps  with  re- 
flectors to  throw  the  light 
upwards  against  the  ceil- 
ing or  against  a  white  dif- 
fusing surface.  Thus  Fig. 
103  shows  an  arc  lamp  with 
an  opal  reflector  for  throw- 
ing the  light  upwards 
against  a  corrugated  dif- 
fuser  having  a  white  enamel 
surface.  This  type  of 
lamp  and  diffuser  is  now 
practically  obsolete;  it  is, 
like  every  other  device  for  indirect  lighting,  too  wasteful. 

80.  Influence    of   absorption   on   illumination. — Everyone   is 
familiar  with  the  fact  that  more  lamps  are  required  to  illuminate 
12 


Fig.  103. 


162  ELECTRIC   LIGHTING. 

a  room  with  dark  walls  than  are  required  to  illuminate  a  similar 
room  with  light  walls.  This  is  because  the  useful  light  in  a  room 
comes,  not  only  directly  from  the  lamps,  but  is  also  reflected 
from  the  walls  and  objects  in  the  room  to  the  object  which  is  in 
the  field  of  vision.  Indeed,  if  all  the  illuminated  surfaces  in  a 
room  could  be  made  to  reflect  all  the  light  which  falls  upon  them, 
then  the  degree  of  illumination  of  the  room  would  increase 
steadily  after  the  turning  on  of  a  lamp;  and  the  ultimate  degree 
of  illumination  would  be  infinitely  great.  The  walls  and  objects 
in  a  room,  however,  always  absorb  light,  and  after  a  lamp  is 
turned  on  the  intensity  of  illumination  in  a  room  increases  quickly 
(almost  instantaneously)  until  the  rate  of  absorption  of  light  by  the 
illuminated  surfaces  is  equal  to  the  rate  of  emission  of  light  by 
the  lamp. 

A  given  surface  absorbs  a  definite  fractional  part  of  the  light 
which  falls  upon  it  and  this  fraction  is  called  the  coefficient  of 
absorption  of  the  surface.  Thus  a  surface  which  absorbs  0.4 
of  the  light  which  falls  upon  it  has  a  coefficient  of  absorption 
equal  to  0.4. 

Let  /  be  the  average  intensity  of  illumination  of  the  walls  and 
objects  in  a  room  in  foot-candles  (lumens  per  square  foot),  let 
A  be  the  area  in  square  feet  of  the  walls  and  objects  in  the  room, 
and  let  k  be  the  average  coefficient  of  absorption  of  the  illu- 
minated surfaces.  Then  A I  is  the  number  of  lumens  of  light 
falling  upon  the  illuminated  surfaces  and  kAI  is  the  number  of 
lumens  absorbed.  That  is  to  say,  the  amount  of  light  which  is 
being  continually  absorbed  is  kAI  lumens,  and  this  must  be 
equal  to  the  total  amount  of  light  L  (in  lumens)  which  is  being 
emitted  by  the  lamps.  Therefore  we  must  have: 

L  =  kAI  (20) 

Example  I—  Consider  one  room  B  which  is  twice  as  long, 
twice  as  wide  and  twice  as  high  as  another  room  A,  the  character 
of  all  surfaces  being  the  same  in  both  rooms,  and  the  furniture 
area  being  four  times  as  great  in  the  larger  room.  Under  these 


INTERIOR   ILLUMINATION.  163 

conditions  the  total  absorption  area  is  four  times  as  great  in  the 
larger  room,  and,  since  the  coefficient  of  absorption  is  assumed  to 
be  the  same,  it  will  take  exactly  four  times  as  much  light  to 
illuminate  the  larger  room  to  the  same  intensity  as  the  smaller 
room.  The  amount  of  light  required  to  illuminate  a  room  to  a 
given  intensity  of  illumination  is  proportional  to  the  total  area  of 
the  illuminated  surfaces,  the  coefficient  of  absorption  being  given. 

Example  2. — According  to  equation  (20)  the  amount  of  light 
required  to  illuminate  a  room  to  a  given  intensity  of  illumination 
is  proportional  to  the  absorption  coefficient  (average)  of  the 
illuminated  surfaces  in  the  room.  Thus  ten  lamps  give  a  desired 
intensity  of  illumination  in  a  given  room  when  the  walls  are  dark 
and  have  a  coefficient  of  absorption  equal  to  0.80.  The  same 
intensity  of  illumination  (average)  will  be  produced  in  the  room 
by  one  half  as  many  lamps  if  the  walls  are  given  a  light  finish  of 
which  the  coefficient  of  absorption  is  0.40. 

Example  j. — A  room  is  15  feet  wide,  20  feet  long  and  12  feet 
high.  The  floor  has  an  area  of  300  square  feet  and  the  effect  of 
furniture  is  to  add,  .say,  150  square  feet  to  this  amount  making  a 
total  area  of  450  square  feet  of  floor  and  furniture.  The  average 
coefficient  of  absorption  of  floor  and  furniture  is  0.88.  The 
coefficient  of  absorption  of  the  ceiling  and  walls  of  the  room  is 
0.40.  Required,  the  number  of  lumens  to  give  an  average  in- 
tensity of  illumination  in  the  room  of  one  foot-candle  (one  lumen 
per  square  foot). 

The  average  coefficient  of  absorption  of  the  illuminated  surfaces 
in  the  room  is  found  approximately  as  follows: 

450  square  feet  X  0.88  =  396 
1,140  square  feet  X  0.40  =  456 

Sum  total  =  852 

Dividing  this  sum  total  by  the  entire  area  of  the  exposed  surfaces 
in  the  room  (1,590  square  feet)  we  have  0.54  as  the  average  value 
of  k.  Therefore,  substituting  in  equation  (20)  A  =  1,590, 


164 


ELECTRIC   LIGHTING. 


k  —  0.54     and     /  =  i.o,     we  find     L  =  852     lumens  or  67.7 
spherical-candles. 

The  method  of  calculating  the  average  coefficient  of  absorption 
of  the  illuminated  surfaces  of  a  room  as  shown  in  this  example  is 
not  strictly  correct,*  but  the  result  of  the  above  calculation  is 
sufficiently  exact  for  most  practical  purposes. 

81.  Calculation  of  light  flux  (lumens)  required  to  illuminate 
a  room. — In  planning  for  the  illumination  of  a  room  equation 
(20)  might  be  used  as  in  example  3  of  Art.  80,  but  in  practice  the 
following  method  is  used. 

INTENSITIES    OF    ILLUMINATION    RECOMMENDED    FOR    VARIOUS 

CLASSES  OF  SERVICE. 

(Foot-candles.) 


Auditorium  or  ball  room 2.0 

Cafe 2.5 

Car,  passenger 2.0 

Car,  mail 7.0 

Church 2.0 

Desk 4.0 

Draughting  and  engraving 7.0 

Factory  and  shop 

(a)  General  illumination 1.5 

(6)  Bench  and  machine-tool  illu- 
mination, local,  in  addition 

to  a 4.0  to  5.0 

(c)  General  illumination  to  take 

the  place  of  a  and  b 3.0  to  5.0 

Garage 2.0 

Library 

Stack  room 1.5 

Reading  room  when  local  desk 
illumination  is  not  supplied  in 

addition 3.5 

Reading  room  when  local  desk 
illumination  is  supplied  in  ad- 
dition   0.7 

Office .  .  4-0 


Stores 

Art 4.0 

Baker 3.0 

Book 3.5 

Butcher 3.5 

China 2.5 

Cigar « 3.0 

Clothing 5.0 

Cloak  &  Suit 5.0 

Confectionery 3.0 

Decorator 3.0 

Department  (see  each  depart- 
ment). 

Drug 3.0 

Dry  goods 4.0 

Florist 3.0 

Furniture 5.0 

Furrier 5.0 

Grocery 3.0 

Haberdasher 3.5 

Hardware 4.5 

Hat 4-0 

Jewelry 3.5 

Lace 3.0 


*  The  correct  expression  for  the  total  amount  of  light  absorbed  is  S£7  -AA, 
where  AA  is  an  element  of  surface,  k  is  its  coefficient  of  absorption,  and  /  is  the 
intensity  of  illumination  at  AA.  Therefore  Z,=S£/-AA;  but  this  formula  would 
lead  to  extremely  tedious  calculations  even  if  all  the  necessary  data  were  known. 


INTERIOR   ILLUMINATION. 


165 


Leather 3.5 

Meat 3.5 

Men's  furnishings 3.5 

Millinery 4.0 

Music 3.0 

Notions 3.0 

Piano 4.0 

Post  cards 3.0 

Show 3.5 

Stationery 3.5 

Tailor 4.0 

Tobacco 3.0 

Street 

Business  streets  ( in  addition  to 
light  from  show  windows  and 

signs) 0.5 

Residence  streets o.i 

Prominent  streets  in  residence 

districts 0.2 

Country  roads 0.05 

Theater 

Lobby 3.0 

Auditorium .  .  .2.0 


Reading  (book  print) 2.0 

Reading  (newspaper  print) 2.5 

Residence 

Porch ^ 0.2 

Porch  (reading  light) i.o 

Hall  (entrance) 0.7 

Reception  room 1.5 

Parlor 1.5 

Sitting  room 1.5 

Library 2.0 

Music  room 2.0 

Dining  room 1.5 

Pantry 2.0 

Kitchen 2.0 

Laundry 1.5 

Hall  (upstairs) 0.5 

Bed  room 1.5 

Bath  room 2.0 

Furnace  room 0.7 

Store  room 0.7 

School  room 2.5 

Shop  (see  factory). 
Show  window 

Light  goods 8.0 

Medium  goods 16.0 

Dark  goods 20.0 

Sign 8.0 

Stable i.o 

(a)  It  is  assumed  that  the  surface  to  be  illuminated  is  a  plane 
at  a  height  of  30  inches  above  the  floor.     This  plane  is  called  the 
working  plane,  and  the  problem  is  to  determine  the  number  of 
lamps  required  to  give  a  specified  average  degree  of  illumination 
on  this  plane.     The  intensities  of  illumination  required  for  various 
kinds  of  service  as  found  from  practice  are  given  in  the  accom- 
panying table.     Multiply  the  desired  intensity  of  illumination  in 
foot-candles  (lumens  per  square  foot)  by  the  area  of  the  working 
p'ane  in  square  feet  to  get  the  required  light  flux  in  lumens. 

(b)  A  certain  fraction,  only,  of  the  light  emitted  by  a  lamp 
reaches  the  working   plane  and   the  accompanying  table  gives 
the  values  of  this  fraction  under  various  conditions.     Divide  the 
total  lumens  required  on  the  working  plane  by  this  fraction  to  get 
the  lumens  delivered  by  the  lamps. 


1 66 


ELECTRIC   LIGHTING. 


(c)  Glow  lamps  are  always  rated  in  mean  horizontal  candle- 
power,  and  to  find  the  total  lumens  delivered  by  a  given  lamp 
one  must  know  the  factor  by  which  mean  horizontal  candle- 
power  must  be  multiplied  to  give  mean  spherical  candle-power. 
The  following  table,  however,  gives  the  rating  in  lumens  of  the 
present  regular  types  of  lamps.  Divide  the  total  lumens  to  be 
delivered  by  the  lamps  by  the  rating  of  the  chosen  type  of  lamp  in 
lumens  to  get  the  number  of  lamps. 

PERCENTAGE  OF  LIGHT  DELIVERED  TO  THE  WORKING  PLANE  BY 
INCANDESCENT  LAMPS.* 

(When  globes  and  reflectors  are  clean.} 


Equipment  of  Lamp. 

Ceiling. 

Walls. 

Percentage. 

Clear  holophane  reflector  

light 

light 

"?7 

Clear  holophane  reflector      

light 

dark 

4C 

Clear  holophane  reflector 

dark 

dark 

og 

No  shade  or  reflector 

light 

light 

on 

No  shade  or  reflector 

light 

dark 

2*1 

Opal  reflector 

light 

light 

co 

Opal  reflector  

light 

dark 

41 

See  pages  147  and  148  for  data  concerning  arc  lamps. 

Example. — It  is  proposed  to  install  electric  lights  in  a  men's 
furnishing  store  80  feet  long,  25  feet  wide  and  12^  feet  high. 
The  ceiling  is  light,  but  the  walls  are  covered  with  shelves  con- 
taining dark  goods,  and  therefore  the  walls  cannot  be  counted 
on  to  reflect  much  light. 

Referring  to  the  table  we  find  that  an  illumination  of  about 
3.5  foot-candles  is  usual  in  stores  of  this  kind,  but  the  store  under 
consideration  is  not  in  a  metropolitan  district  where  comparisons 
would  be  made,  and  therefore  3.0  foot-candles  may  be  taken  as  a 
sufficient  degree  of  illumination. 

The  chosen  degree  of  illumination  of  3.0  foot-candles  (or 
3  lumens  per  square  foot)  is  to  be  produced  over  the  "working 

*  From  the  publications  of  the  Holophane  Company.  The  percentage  is  less 
for  a  tungsten  lamp  than  for  a  carbon-filament  lamp  especially  when  the  lamps 
are  bare.  The  table  refers  primarily  to  tungsten  lamps  and  the  values  may  be 
used  for  carbon  lamps  without  serious  error. 


INTERIOR   ILLUMINATION. 


I67 


plane"    which    contains    2,000    square    feet.     Therefore    6,000 
lumens  of  light  are  required  on  the  working  plane. 

TOTAL   LUMENS   GIVEN    BY   REGULAR   TYPE  LAMPS.* 

This  table  gives  the  total  light  emitted  by  regular  type  lamps  when  operated  at 
"top  efficiency."  Light  is  expressed  in  lumens.  For  ratings  of  arc  lamps  (in 
downward  lumens)  see  pages  147  and  148. 


Rated 
Watts. 

Tungsten. 

Tantalum. 

Metallized 
Carbon. 

Carbon. 

100-130 

Volts. 

200-260 
Volts. 

100—130 

Volts. 

200-260 

Volts. 

100-130 

Volts. 

100-130 

Volts. 

200-260 
Volts. 

IO 











21 



IS 

no 













2O 

150 









50 



25 

185 



125 





84 



30 









105 

96 



35 













84 

40 

320 

300 

220 



160 





So 





275 

250 

205 

175 



60 

5OO 

455 





250 

210 

170 

80 





445 

4OO 

335 





100 

830 

760 

420 

350 



120 







420 

340 

125 





525 

ISO 

1,250 

i,i37 



187.5 





785 

250 

2,I7O 

i,895 

1,050 

40of 

3,520 



Soof 

4,400 

4,030 

It  is  intended  to  use  tungsten  lamps  with  holophane  reflectors, 
and  according  to  the  above  table  such  lamps  so  equipped  deliver 
45  per  cent,  of  their  light  to  the  working  plane  in  a  room  with 
light  ceiling  and  dark  walls.  Therefore  the  total  amount  of 
light  to  be  delivered  by  the  lamps  is  13,333  lumens. 

Dividing  the  total  lumens  by  the  rating  of  the  various  sizes 
of  tungsten  lamps  as  given  in  the  above  table,  we  find  that  the 
required  average  degree  of  illumination  of  the  working  plane 
would  be  produced  by  any  of  the  following: 

*  This  table  is  taken  from  the  publications  of  the  General  Electric  Company 
and  it  is  standard  at  this  date,  April  i,  1912.  The  table  is  reissued  by  the  company 
whenever  changes  are  made  in  the  ratings  of  regular  lamps. 

t  Round  bulb  lamps;  all  other  lamps  in  the  table  have  regular  type  bulbs. 


1 68  ELECTRIC   LIGHTING. 

seventy-two  25-watt  tungsten  lamps, 

forty-two  4O-watt  tungsten  lamps, 

twenty-seven  6o-watt  tungsten  lamps, 

sixteen  loo-watt  tungsten  lamps, 

eleven  150- watt  tungsten  lamps, 

six  25O-watt  tungsten  lamps, 

or                 three  5oo-watt  tungsten  lamps, 

The  choice  of  size  of  lamp  is  considered  in  the  following  article, 
where  this  example  is  carried  to  a  conclusion. 

82.  The  choice  of  size  of  lamps. — Economy  in  first  cost  and 
economy  in  operation  leads  one  to  choose  the  largest  size  lamps 
that  can  be  used  in  a  given  room,  and  the  limit  of  size  is  deter- 
mined by  the  necessity  of  producing  a  fairly  uniform  illumination 
of  the  working  plane.  In  general  the  higher  the  ceiling  the  larger 
the  lamps  that  can  be  used  to  give  satisfactory  illumination. 
The  following  rules  relating  to  spacing  and  heights  of  lamps  serve 
as  a  basis  for  choice  of  size  of  lamps.  These  rules  have  been 
formulated  by  the  engineers  of  the  Holophane  Company. 

Rule  a. — In  narrow  stores  a  single  row  of  lamps  may  be  used. 
In  this  case  the  lamps  should  be  equipped  with  extensive  re- 
flectors, the  height  H  of  the  lamps  above  the  working  plane 
should  be  from  four  tenths  to  five  tenths  of  the  width  of  the 
room,  and  the  distance  apart  s  of  the  lamps  should  not  exceed 
two  times  their  height  above  the  working  plane. 

Rule  b. — In  large  rooms  with  unusually  high  ceilings,  divide 
the  space  as  nearly  as  possible  into  equal  squares,  place  a  lamp 
,at  the  center  of  each  square,  use  focusing  reflectors,  and  make 
fthei  height  of  lamps  above  the  working  plane  equal  to  about  one 
.and  one. third 'times  their  distance  apart. 

Rule  c. — in  large  rooms  .with  ordinary  ceiling  heights  or  in 
stores  in  which  it  is  intended  to  use  two  or  more  rows  of  lamps, 
place  lamps  according  to  rule  &,  but  use  intensive  reflectors  and 
make  the  height  of  lamps  above  the  working  plane  equal  tp 
four  fifths  pf  their  distance  apart. 


INTERIOR   ILLUMINATION. 


169 


Where  architectural  restrictions  make  it  impossible  to  follow 
this  rule,  the  height  of  lamps  above  the  working  plane  may  be 
varied  from  0.66  to  i.o  times  their  distance  apart  without 
seriously  affecting  the  uniformity  of  illumination  on  the  working 
plane. 

Rule  d. — Where  outlets  are  located  too  far  apart  for  rule  c, 
or  where  it  is  found  impracticable  to  supply  as  many  outlets 
as  rule  c  requires,  divide  the  room  into  approximately  equal 
squares,  place  a  lamp  at  the  center  of  each  square,  use  extensive 
reflectors  and  make  the  height  of  the  lamps  above  the  working 
plane  approximately  one  half  their  distance  apart. 

Example. — The  example  given  in  Art.  81  may  now  be  carried 
to  a  conclusion.  The  given  room  is  I2j^  feet  high,  and  the 
working  plane  is  2^/2  feet  above  the  floor.  It  does  not  look  well 
to  place  lamps  close  up  against  the  ceiling;  therefore  let  the 
lamps  be  placed  one  foot  below  the  ceiling.  This  gives  a  height 
of  9  feet  (=  H)  above  the  working  plane.  The  lamps  with 
the  chosen  type  of  reflectors  (intensive  reflectors)  should  there- 
fore be  II  feet  apart  (=  s  =  5/4  #).  Consequently  the  room 
should  be  divided  into  squares  approximately  1 1  feet  X  1 1  feet. 

< 80-  feet >- 


4 

"V 

4       4 

i 

4 

4   I  -0- 

i 

4 

f 

1 

i 

or 

4 

r 

4 

i 

4 

<i>  i  4. 

i 

1 
1 

1 

n 


Fig.  104. 

Therefore  the  room  may  be  divided  into  16  squares  as  shown 
Fig.    104  each   square  being   10  feet  X  I2j^  feet,   and  the 
^desired  quantity  of  light  would  be  produced  by  placing  a  100- 
-watt  tungsten  lamp  at  the  center  of  each  square  (see  Art.  81), 
or  the  room  may  be  divided  into  12  squares  each  13.3  feet  X  I2j^ 
ieet  _and  the  ^desired  quantity  of  light  would  ,be  produced  by 


170  ELECTRIC   LIGHTING. 

placing  a  150- watt  tungsten  lamp  at  the  center  of  each  square. 
The  sixteen  loo-watt  lamps  would  give  a  slightly  more  satis- 
factory illumination,  but  the  twelve  150- watt  lamps  would 
be  slightly  cheaper  to  install.  Either  arrangement  would  be 
satisfactory. 


CHAPTER    VII. 
• 

STREET  LIGHTING. 

83.  Detail  vision  and  block  vision. — Every  one  knows  that 
to  see  the  fine  details  of  an  object  one  must  look  directly  at 
the  object.  Let  the  reader  fix  his  eyes  on  this  single  letter  A 
and  consider  how  narrow  his  field  of  acute  vision  really  is;  it 
is  scarcely  possible  to  recognize  any  of  the  surrounding  letters 
while  looking  directly  at  A.  Everyone  knows  also  how  quickly 
one  sees,  for  example,  a  hand  which  is  moved  up  along  side  of 
one's  head  from  behind,  although  one  may  have  to  turn  and 
look  directly  at  the  hand  before  one  recognizes  that  it  is  a  hand. 

That  kind  of  vision  where  one  looks  directly  at  an  object 
and  sees  minute  detail  may  be  called  detail  vision,  and  that 
kind  of  vision  where  one  sees  things  without  minute  detail 
may  be  called  block  vision.  Detail  vision  requires  strong  illu- 
mination and  the  field  of  detail  vision  is  very  narrow.  Block 
vision  does  not  require  strong  illumination  and  the  field  of 
block  vision  is  very  wide.  In  fact  block  vision  is  very  good  when 
the  intensity  of  illumination  is  0.02  of  a  foot-candle,  which  is  the 
intensity  of  illumination  in  full  moon  light.  An  important  char- 
acteristic of  block  vision  in  very  dim  light  is  that  the  eye  must 
be  kept  in  the  dark;  after  a  momentary  exposure  of  the  eye  to 
bright  light  one  can  scarcely  see  at  all  in  very  dim  light,  and  the 
blinding  effect  of  the  bright  light  lasts  for  five  minutes  or  more. 
Block  vision  in  very  dim  light  is  sometimes  called  twilight  vision. 

Two  kinds  of  organs  are  recognized  in  the  retina  of  the  eye,  namely,  the  rods 
which  are  distributed  over  the  whole  retina  except  a  small  central  spot  which  is 
called  the  fovea,  and  the  cones  which  are  crowded  together  in  great  numbers  in  the 
fovea  and  which  are  distributed  rather  sparsely  over  the  remainder  of  the  retina. 
To  see  the  fine  details  of  an  object  the  image  of  the  object  must  fall  on  the  fovea, 
The  fovea  is  used  for  detail  vision  and  the  remainder  of  the  retina  is  used  for  block 
vision;  or  the  cones  are  used  for  detail  vision  and  the  rods  are  used  for  block  vision.* 

*  This  statement  is  perhaps  not  strictly  correct.  An  interesting  discussion  of 
vision,  including  color  vision,  is  given  by  Percy  W.  Cobb  on  pages  525-574.  Vol.  II, 
Johns  Hopkins  University  Lectures  on  Illuminating  Engineering,  Baltimore,  1911. 

I/I 


172  ELECTRIC    LIGHTING. 

Therefore  detail  vision  is  sometimes  called  cone  vision,  and  block  vision  is  some- 
times called  rod  vision. 

84.  Intensity  of  illumination  required  for  street  illumination.* 

— The  intensity  of  illumination  required  for  interior  lighting 
varies  from  one  to  five  or  six  foot-candles  (see  table  on  page  164), 
and  this  brilliant  illumination  is  required  because  it  is  detail 
vision  that  must  be  provided  for;  furthermore  the  perception  of 
colors  requires  brilliant  illumination,  in  very  dim  light  all  color 
differences  disappear.  It  is  out  of  the  question  to  provide  street 
illumination  sufficiently  bright  to  give  complete  detail  vision 
and  color  vision,  the  cost  would  be  prohibitive. 

It  is  customary  in  the  discussion  of  street  lighting  to  specify 
intensity  of  illumination  normal  to  beam.  This  quantity  is  repre- 
sented by  the  symbol  In;  see  Art.  52.  Furthermore,  an  intensity 
of,  say,  0.05  foot-candle  of  normal  illumination  at  a  point  mid- 
way between  two  street  lamps  is  understood  to  mean  0.05  due 
to  each  lamp.  The  intensities  of  illumination  actually  used  for 
street  lighting  range  from  o.oi  foot-candle  (average)  to  o.i  foot- 
candle  (average)  in  well  lighted  cities,  as  follows: 

(a)  Streets   where   the   night   traffic   is   heavy   require   good 
illumination,  as  do  also  certain  streets  where  criminal  disturbances 
are  likely  to  occur.     For  such  streets  a  minimum  of  0.05  foot- 
candle  (normal  to  the  beam)  and  an  average  of  o.i  foot-candle 
is  quite  satisfactory. 

(b)  Ordinary  residence  streets  and  streets  where  the  night 
traffic  is  light  are  satisfactorily  lighted  if  an  average  of  0.05 
foot-candle  with  a  minimum  of  0.025  foot-candle   (normal  to 
beam)   is   provided.     Streets  so  lighted  are  as  bright  as  full 
moonlight  at  the  darkest  places. 

(c)  Streets  where  the  houses  are  scattering  and  where  there 
is  very  little  night  traffic  are  satisfactorily  lighted  when  a  mini- 
mum of  o.oi  foot-candle  (normal  to  beam)  is  provided,  and  the 

*  A  very  good  discussion  of  this  matter  is  given  by  Louis  Bell  on  pages  795-837- 
Vol.  II,  Johns  Hopkins  University  Lectures. on. Illuminating,  Engineering,  Baltimore, 
.1911. 


STREET   LIGHTING.  173 

effectiveness  of  this  dim  illumination  is  very  greatly  increased 
by  placing  the  lamps  (small  lamps,  of  course)  high  overhead  so 
as  to  avoid  local  regipns  of  intense  illumination  which  tend  to 
destroy  the  extreme  sensitiveness  of  the  eye  in  very  dim  light 
as  stated  in  Art.  83. 

A  condition  which  favors  vision  on  a  street  at  night  is  as 
follows:  When  one  is  at  a  dimly  lighted  part  of  the  street  one 
sees  a  dark  object  on  the  street  projected  against  the  brightly 
illuminated  field  near  a  distant  lamp. 

85.  Arc  lamps  for  street  lighting. — Everyone  is  familiar  with 
the  street  arc  lamp.  In  the  earlier  days  this  was  an  open  carbon- 
arc  lamp  operated  by  direct-current  from  a  Brush  or  Thomson- 
Houston  generator.  Later  the  enclosed  carbon-arc  lamp  was 
extensively  used  for  street  lighting,  and  in  some  cases  these 
carbon-arc  lamps  (open  and  enclosed)  were  operated  by  alternat- 
ing current.  In  new  installations  magnetite-arc  lamps  are  most 
extensively  used,  and  the  long-burning  flame-arc  lamp  (the 
enclosed  flame-arc  lamp)  and  the  quartz  tube  mercury-vapor 
lamp  are  coming  into  use. 

Arc  lamps  are  suitable  only  for  streets  which  are  to  be  brightly 
lighted,  and  for  ordinary  first  class  street  illumination  (minimum 
0.05  foot-candle,  average  o.i  foot-candle  normal  to  beam)  the 
4-ampere  magnetite-arc .  lamp  is  perhaps  the  most  economical. 

Very  high  candle-power  lamps  are  wasteful  for  street  lighting 
(unless  very  brilliant  illumination  is  desired)  even  when  they  are 
placed  very  high  above  the  street,  because  the  diameter  of  the 
circular  field  illuminated  by  such  a  lamp  is  usually  three  or  four 
or  five  times  the  width  of  the  street. 

A  street  with  many  trees  cannot  be  properly  lighted  by  arc 
lamps  at  a  reasonable  cost;  such  streets  should  be  lighted  by 
many  small  lamps  (tungsten  lamps). 

A  street  lamp  should  give  the  greater  part  of  its  light  in  a 
direction  slightly  below  the  horizontal.  Thus  the  magnetite-arc 
lamp  (curves  3  and  4,  Fig.  94  a)  and  the  vertical-carbon  long- 


174 


ELECTRIC   LIGHTING. 


burning  flame-arc  lamp  (curve  7,  Fig.  94  b)  are  well  adapted  to 
street  lighting. 

Arc  lamps  are  not,  as  a  rule,  hung  sufficiently  high  on  the 
streets  of  American  cities,  the  usual  practice  being  to  hang  the 
4-ampere  magnetite-arc  lamp  20  or  25  feet  above  the  street  and 
the  6.6-ampere  magnetite-arc  lamp  25  or  30  feet  above  the  street. 


0.6 


A — A 


0-4 


\ 


7 


Fig.  105. 

The  ordinates  of  the  curves  3,  4,  and  7  in  Fig.  105  show  the 
values  of  Jn  (intensity  of  illumination  normal  to  beam)  at  various 
horizontal  distances  along  a  street  from  the  various  lamps,  the 
heights  of  the  lamps  above  the  street  being  30  feet,  40  feet, 
and  50  feet  respectively,  as  represented  by  the  small  crosses  in 
the  figure.  The  values  of  In  are  reckoned  at  the  surface  of 
the  street.  The  inclined-carbon  flame-arc  lamp  is  not  adapted 
to  ordinary  street  lighting. 

The  accompanying  table  gives  the  values  of  In  at  points  on  a 
street  distant  x  feet  horizontally  from  the  various  kinds  of  lamps, 
the  height  of  the  lamp  in  each  case  being  50  feet. 


STREET    LIGHTING. 


175 


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I76 


ELECTRIC   LIGHTING. 


By  making  use  of  the  law  of  inverse  squares  (Art.  48)  it  Is 
easy  to  use  this  table  to  find  the  intensity  of  illumination  (normal 
to  beam)  at  a  point  on  the  street  at  any  given  distance  d  hori- 
zontally from  any  one  of  the  lamps  placed  at  any  given  height  H 
above  the  street.  The  rule  is  as  follows:  Find  from  the  table  the 
value  of  Jtt  for  the  lamp  50  feet  high  and  for  x  —  d  X  5O/ Ht  and 
multiply  the  value  of  /n  so  found  by  (5O/  H)z. 


Fig.  106. 

Also  the  table  can  be  used  to  find  the  horizontal  distance  d 
from  a  lamp  ( H  feet  above  the  street)  to  the  point  on  the  street 
where  the  normal  illumination  has  a  prescribed  value.  The  rule 
is  as  follows:  Multiply  the  prescribed  normal  illumination  by 
( H/$o)2  to  get  In  as  per  table,  find  the  corresponding  value  of  x 
from  the  table  and  multiply  this  value  of  x  by  (H/^o)  to  get  the 
desired  value  of  d. 

86.  Glow  lamps  for  street  lighting. — The  great  advantage  of 
glow  lamps  for  street  lighting  is  that  a  fairly  uniform  distribution 
of  light  along  a  street  can  be  produced  much  cheaper  by  small 
lamps  than  by  large  lamps.  Tungsten  lamps,  for  example, 
equipped  with  suitable  reflectors  (see  below)  and  properly  spaced 
along  a  street  give  an  illumination  which  is  entirely  satis- 


STREET   LIGHTING. 


177 


factory  for  residence  and  suburban  districts,  and  the  cost  is 
less    perhaps    than    any   other   kind    of    street 
lighting.  ^  ^ 

Figure  106  shows  a  common  form  of  sus- 
pension fixture  and  reflector  for  a  tungsten 
street  lamp.  The  reflector  is  made  of  sheet 
metal  with  a  white  enamel  surface,  and  it  has 
radial  flutings.  Figure  107  shows  an  ornamental 
street  lighting  cluster  of  tungsten  lamps  mounted 
on  top  of  a  post  and  equipped  with  holophane 
street  reflectors. 

The  dotted  curve  in  Fig.  108  shows  the  dis- 
tribution of   candle-power  around  a  4O-candle- 
power  tungsten  lamp  without  a  shade,  and  the  full-line  curve 
shows    the    distribution    of    candle-power   of   the   same   lamp 
equipped  as  shown  in  Fig.  106. 


Fig.  107. 


Fig.  108. 

For  sidewalk  lighting  32-candle-power  or  4O-candle-power 
tungsten  lamps  are  usually  employed  and  hung  10  or  12  feet 
above  the  walk.  For  street  lighting  larger  tungsten  lamps  are 

'3 


178 


ELECTRIC    LIGHTING. 


used  and  they  are  hung  over  the  middle  of  the  street  at  heights 
of  from  1 8  to  24  feet  above  the  street. 


surface  of  street 


k 


Fig.  109. 


NORMAL   ILLUMINATION   IN  FOOT-CANDLES  DUE  TO  40-CANDLE- 
POWER  TUNGSTEN  LAMP  *  WITH  RADIAL  REFLECTOR  AS 
SHOWN  IN  FIG.   106  OR  108. 


Height  of  Lamp  H. 

10  Feet. 

12  Feet. 

15  Feet. 

18  Feet. 

0 

0.260 

O.lSl 

O.II5 

0.0803 

.60            5 

0.288 

O.2OI 

O.I27 

0.0860 

<u  +*    IO 

O.222 

0.174 

0.123 

0.0884 

to    4J     15 

0.146 

0.125 

0.0985 

0.0774 

^  C     20 

0.098 

0.0882 

0.0744 

O.O622 

<uX  25 

O.O688 

0.0637 

0.0565 

0.0496 

c  o^  35 

0.0383 

0.0368 

0.0342 

0.0316 

S  w  5° 

0.0196 

0.0193 

O.OI85 

0.0177 

3     75 

0.00856 

O.OO875 

O.OO872 

0.00858 

100 

0.00466 

0.00483 

0.00489 

O.OO492 

From  this  table  the  normal  illumination  at  any  point  on  a 
street  produced  by  a  tungsten  lamp  of  any  candle-power  C 
(equipped  like  Fig.  106)  can  be  found  by  multiplying  the  tabu- 
lated value  of  In  by  C/4O. 

If  it  is  desired  to  find  the  intensity  of  illumination  (normal) 
produced  at  a  distance  d  horizontally  from  a  lamp  hung  // 

*  This  table  refers  specifically  to  the  special  low-voltage  tungsten  lamp  which 
is  described  on  page  143  and  shown  in  Fig.  93.  the  lamp  being  equipped  with  a 
"radial  wave  "  reflector  as  shown  in  Fig.  106. 


STREET    LIGHTING.  179 

feet  above  the  street,  the  method  used  in  Art.  85  can  be  em- 
ployed as  shown  by  the  following  examples: 

Example  I . — What«is  the  normal  illumination  at  a  point  on  the 
street  distant  150  feet  from  a  2OO-candle-power  lamp  like  Fig.  106, 
the  lamp  being  24  feet  above  the  street.  Divide  the  given 
distance  (150  feet)  and  the  given  height  (24  feet)  by  some  factor 
b  to  give  a  height,  say,  of  12  feet  which  appears  in  the  table. 
In  this  case  b  =  2.  Find  In  from  the  table  for  this  reduced 
distance  (75  feet)  and  reduced  height  (12  feet),  and  divide  the 
value  of  In  so  found  by  b2.  This  gives  the  normal  illumination 
which  would  be  produced  by  a  4O-candle-power  lamp  at  a 
distance  of  150  feet,  the  height  of  the  lamp  being  24  feet;  and 
if  we  multiply  this  by  200/40  we  have  the  desired  result,  namely, 
0.0109  foot-candle. 

Example  2. — How  far  apart  must  2oo-candle-power  tungsten 
lamps  (like  Fig.  1 06)  hung  24  feet  above  the  street  be  placed  to 
give  a  minimum  of  0.025  foot-candle  (normal)  at  a  point  on  the 
street  midway  between  two  lamps.  Let  2d  be  the  desired 
spacing,  then  the  problem  is  to  find  the  distance  d  from  a  200- 
candle-power  tungsten  lamp  for  which  the  normal  illumination 
due  to  the  lamp  is  0.025  foot-candle.  Divide  the  specified  height 
(24  feet)  and  the  distance  d  by  a  factor  b  which  will  reduce  the 
height  to  say  12  feet  which  appears  in  the  table.  In  this  case 
the  value  of  b  is  2.  Multiply  the  desired  illumination,  0.025,  by 
40/200  to  get  the  illumination  which  would  be  given  by  a  40- 
candle-power  lamp.  Multiply  this  result  by  b2  (=4)  to  get  the 
illumination  (0.020)  corresponding  to  reduced  height  (12  feet) 
and  reduced  distance  (dJ2\.  Find  the  value  of  x  from  the 
table  corresponding  to  a  height  of  12  feet  and  an  illumination  of 
0.02.  This  value  of  x  (which  is  found  to  be  a  little  less  than 
50  feet)  is  equal  to  d/2.  Therefore  the  desired  spacing  (2d)  is 
a  little  less  than  200  feet. 

87.  Systems  of  street  lighting. — The  kinds  of  lamps  used  for 
street  lighting  are  mentioned  in  Arts.  85  and  86.  It  remains 


i8o 


ELECTRIC   LIGHTING. 


to  discuss  the  methods  of  connecting  the  lamps  in  groups  and 
the  mode  of  delivery  of  current  to  the  groups  of  lamps. 

Single  arc  lamps  are  always  connected  across  constant-voltage 
supply  mains.  Such  lamps  are  called  multiple  lamps  as  stated 
in  Art.  71.  Multiple  lamps  are  seldom  used  for  street  lighting. 


suspension 


A  C  arc  lamps  in   series 


constant  current 


A  C    supply 
constant  voltage 


Fig.  110. 


When  a  great  number  of  arc  lamps  are  used  in  one  installation, 
the  lamps  are  always  designed  to  be  operated  in  series;  and  a 
group  of  lamps  in  series  must  be  operated  by  a  constant  current. 
In  the  early  days  of  electric  street  lighting  the  constant  current 
for  operating  arc  lamps  in  series  was  supplied  by  a  "constant- 
current"  generator  of  the  direct-current  type,  but  this  arrange- 
ment is  now  obsolete.  New  arc-lamp  street  lighting  installations 
are  now  series  magnetite-arc  lamps  operated  by  constant  direct 
current  derived  from  a  constant-voltage  alternating  source  by 
means  of  the  constant-current  transformer  and  the  mercury  vapor 
rectifier.  Flame-arc  lamps  can  be  operated  by  direct  current 
and  these  lamps  (if  they  have  the  proper  current  rating)  can  be 
operated  in  series  with  magnetite-arc  lamps.  A  large  group  of 
flame-arc  lamps  would  be  most  conveniently  operated  by  a  con- 
stant alternating  current  derived  from  a  constant- voltage  supply 
by  means  of  the  constant-current  transformer. 

Figure  no  shows  the  scheme  for  supplying  a  group  of  series 
arc  lamps  with  constant  alternating  current  derived  from  a 
constant-voltage  supply.  The  lamps  used  in  this  case  cannot  be 
magnetite-arc  lamps  because  such  lamps  cannot  be  operated 
by  alternating  current.  Figure  in  shows  the  scheme  for  supply- 


STREET   LIGHTING. 


181 


ing  a  group  of  series  arc  lamps  with  constant  direct  current 
derived  from  a  constant-  voltage  alternator.  The  lamps  used  in 
this  case  may  be  magnetite-arc  lamps  or  flame-arc  lamps  or 
both.  A  general  view  of  a  constant-current  transformer  is 
shown  in  Fig.  112.  This  transformer  has  a  movable  secondary 
coil  which  is  delicately  counterpoised.  When  one  or  more  lamps 
are  taken  out  of  service  (by  short-circuiting,  or  by-pass  switches) 
the  tendency  is  for  the  current  to  increase  but  this  tendency  is 
counteracted  by  the  movement  of  the  secondary  coil. 


constant-  current   transformer 


D  C  arc  lamps  in  series 


mercury-  vapor 
rectifier 


constant  current 


Fig.  Ill 

Glow  lamps  for  street  lighting  are  sometimes  connected  in 
parallel  to  constant-voltage  supply  mains  in  the  same  way  that 
house  lamps  are  usually  connected.  In  fact  this  arrangement  is 
always  used  when  a  very  few  glow  lamps  are  used  at  widely  sepa- 
rated parts  of  a  town  or  city.  The  lamps  are  connected  across 
the  low-voltage  terminals  of  a  transformer  which  supplies  the 
neighboring  houses. 

When  many  glow  lamps  are  used  on  the  streets  of  a  town  or 
city  the  lamps  are  always  connected  in  series,  and  two  different 
schemes  are  employed  to  supply  current  to  such  series  groups  of 
lamps  as  follows: 


1 82 


ELECTRIC    LIGHTING. 


(a)  The  series  group  may  be  connected  directly  to  the  constant- 
voltage  bus  bars  in  the  station.  Thus  twenty  no-volt  lamps 
may  be  connected  in  series  to  a  2,2OO-volt  supply.  In  this  case 
provision  must  be  made  to  place  an  auxiliary  lamp  in  circuit  when 
one  of  the  service  lamps  breaks,  as  explained  in  connection  with 
Figs.  1 8  and  19  in  Chapter  II. 


Fig.  112. 

(b)  Each  series  group  of  lamps  may  be  supplied  with  a  constant 
alternating  current  derived  from  a  constant-voltage  source  by 
means  of  a  constant-current  transformer  exactly  as  in  the  case  of 
a  series  group  of  alternating-current  arc  lamps  as  represented  in 
Fig.  1 10.  In  this  case  provision  must  be  made  to  close  a  by-pass 
around  a  lamp  which  burns  out  or  is  broken.  This  is  accom- 
plished exactly  as  explained  in  connection  with  Figs.  18  and  19 
in  Chapter  II,  except  that  no  auxiliary  lamp  is  used. 

Operation  of  lamps  of  different  current  ratings  in  a  series  circuit 
using  alternating  current. — Given  a  series  group  of  arc  lamps 


STREET   LIGHTING.  183 

operated  by,  say,  12  amperes  alternating  current.  A  series  group 
of  lamps  of  any  current  rating  may  be  operated  in  conjunction 
with  the  given  group  by  connecting  as  shown  in  Fig.  113.  A 


constant  -current  glow  lamp  circuit 

tratt*former 


-X 

constant-current  arc  lamp   circuit 


transformer*  connected  as  shown  in  Fig.  113  gives  a  secondary 
current  which  is  equal  to  Z'/Z"  times  the  primary  current,  where 
Z'  and  Z"  are  the  numbers  of  turns  of  wire  in  primary  and1 
secondary  coils  respectively. 

Increased  cost  of  power  due  to  the  use  of  constant-current  trans- 
former and  rectifier. — A  slight  addition  to  the  cost  of  power  is 
involved  in  the  use  of  the  constant-current  transformer  and 
rectifier  on  account  of  the  interest  on  the  cost  of  the  transformer 
and  rectifier,  depreciation  of  non-renewable  parts,  cost  of  renewals 
of  rectifier  bulbs,  and  loss  of  energy  in  transformer  and  rectifier. f 

*It  is  distinctly  misleading  to  call  this  transformer  a  "  series  "  transformer. 
It  is  simply  an  ordinary  transformer. 

t  See  Bulletin  No.  51  of  the  Illinois  Engineering  Experiment  Station  (Bryant 
and  Hake),  pages  46-47. 


CHAPTER  VIII. 

ELECTROLYSIS  AND    BATTERIES. 

88.  Electrolysis.* — Two  sheets  of  copper  A  and  C,  Fig.  114, 
dipping  into  a  solution  of  copper  sulphate  are  connected  to  direct- 
current  supply  mains  as  shown  and  the  flow  of  electric  current  is 
indicated  by  the  arrows.  During  the  flow  of  current  the  copper 
plate  A  is  slowly  dissolved  and  metallic  copper  is  slowly  de- 
posited upon  the  plate  C. 

The  slow  dissolving  of  the  plate  A  and  the  slow  deposition  of 
metallic  copper  upon  plate  C  are  evidences  of  chemical  action 
at  A  and  C.  Chemical  action  thus  produced  by  the  electric 
current  is  called  electrolysis,  the  solution  through  which  the 
current  flows  is  called  an  electrolyte,  the  arrangement  VV  is 

*  The  methods  of  electroplating  and  electrotyping  are  described  by  Samuel  Field 
in  Principles  of  Electrodeposition,  Longmans,  Green  &  Co.,  1911.  The  most  com- 
plete discussion  of  this  subject  is  Electrolytische  Metallniederschldge,  by  W.  Pfan- 
hauser,  Jr.,  Berlin,  1910.  See  also  Handbuch  der  electrolytischen  Metallniederschldge 
by  Georg  Langbein,  Leipzig,  1906. 

The  electrolytic  refining  of  copper  is  a  simple  process  of  electroplating  in  which 
pure  copper  is  deposited  out  of  a  solution  while  the  impurities  are  left  in  the  solu- 
tion. See  Electrochemical  and  Metallurgical  Industry  (now  Metallurgical  and  Chem- 
ical Engineering},  Vol.  I,  pages  561-562,  December,  1903. 

The  extraction  of  aluminum  from  bauxite  is  described  by  Joseph  W.  Richards, 
Electrochemical  and  Metallurgical  Industry  (now  Metallurgical  and  Chemical 
Engineering),  Vol.  I,  pages  158-162,  Jan.,  1903. 

The  electrolytic  manufacture  of  alkali  and  chlorine  is  described  by  L.  E.  Baeke- 
land,  Metallurgical  and  Chemical  Engineering,  Vol.  V,  pages  209-212,  June,  1907. 

The  manufacture  of  chlorates  by  electrolysis  is  described  by  G.  Rossert. 
L'Eclairage  Electrique,  beginning  July  27,  1907. 

The  manufacture  of  metallic  sodium  and  of  sodium  peroxide  is  described  in  the 
Electrochemical  and  Metallurgical  Industry  (now  Metallurgical  and  Chemical  Engi- 
neering), Vol.  I,  pages  n-22,  Sept.,  1903. 

Electrolysis  is  used  extensively  for  recovering  tin  from  tinned  iron  scrap,  for 
refining  gold  and  silver,  and  for  reducing  lead  ore.  Most  of  these  processes  are 
described  in  the  Metallurgical  and  Chemical  Engineering 

184 


ELECTROLYSIS   AND    BATTERIES. 


185 


D  C  supply 
mains 


rheostat 


called  an  electrolytic  cell  and  the  copper  plates  A  and  C  are 
called  electrodes.  The  electrode  A  at  which  the  current  enters 
the  solution  is  called  £he  anode,  and  the  electrode  C  at  which  the 
current  leaves  the  solution  is  called  the  cathode. 

Solutions  of  acids  and  salts  generally  are  electrolytes,  also 
fused  salts  are  electrolytes.  That  is  to  say,  the  flow  of  electric 
current  through  such  a  solution  or 
through  a  fused  salt  produces  chem- 
ical action  at  the  point  where  the 
current  enters  the  liquid  (at  the 
anode)  and  at  the  point  where  the 
current  leaves  the  liquid  (at  the 
cathode) . 

A  good  example  of  electrolysis  is 
the  electrolysis  of  a  solution  of  hy- 
drochloric acid  (HC1)  between  elec- 
trodes of  carbon.  In  this  case 
hydrogen  (H)  is  liberated  at  the 
cathode  and  chlorine  (Cl)  is  liber- 
ated at  the  anode.  In  general  the 
molecule  of  any  dissolved  salt  or 
acid  is  separated  into  two  parts  by 

electrolysis ;  one  part  is  liberated  at  the  cathode  and  is  called  the 
cathion,and  the  other  part  is  liberated  at  the  anode  and  is  called 
the  anion.  Thus  hydrogen  (H)  is  the  cathion  and  chlorine  (Cl) 
is  the  anion  of  hydrochloric  acid.  In  all  metallic  salts  the  metal 
constitutes  the  cathion  and  the  acid  radical  or  halogen  consti- 
tutes the  anion.  In  acids  the  hydrogen  constitutes  the  cathion 
and  the  acid  radical  or  halogen  constitutes  the  anion.  Thus  in 
the  case  of  copper  sulphate  (CuSO4)  the  cathion  is  copper  (Cu), 
and  the  anion  is  the  acid  radical  (SO4) . 

The  dissociation  theory  of  electrolysis.* — Many  of  the  known  facts  of  electrolysis 
*  The  dissociation  theory  is  used  very  extensively  in  advanced  treatises  in  the 
correlation  of  experimental  results.  A  good  discussion  of  this  subject  is  given  in 
Chapter  7  of  Nernst's  Theoretical  Chemistry,  Macmillan  and  Co.  See  also  Chapters 
9-12  of  Whetham's  Theory  of  Solution,  Cambridge  University  Press.  A  good  dis- 
cussion of  electrolysis  is  also  given  in  H.  C.  Jones'  Elements  of  Physical  Chemistry, 
The  Macmillan  Co. 


Fig.  114. 


1 86  ELECTRIC    LIGHTING. 

may  be  clearly  conceived  in  terms  of  the  dissociation  theory  which  is  briefly  as 
follows:  Consider  a  solution  of  common  salt  (NaCl)  for  example.  Every  molecule 
of  the  salt  in  a  dilute  solution  is  supposed  to  be  separated  into  positively-charged- 
sodium-atoms  ( +  Na)  and  negatively-charged-chlorine-atoms  ( —  Cl)  which  are 
called  ions.  The  positively  charged  sodium  atoms  are  called  cathions,  and  the 
negatively  charged  chlorine  atoms  are  called  anions.  Ordinarily  these  ions  wander 
about  in  the  solution,  but  the  application  of  an  electromotive  force  to  the  electrodes 
produces  an  electric  field  throughout  the  solution,  and  the  forces  exerted  on  the 
ions  by  this  electric  field  cause  the  cathions  to  drift  towards  the  cathode  and  the 
anions  to  drift  towards  the  anode.  When  the  cathions  reach  the  cathode  they  give 
up  their  positive  charges  and  enter  into  chemical  combination  or  are  deposited  as 
neutral  metal  or  hydrogen;  when  the  anions  reach  the  anode  they  give  up  their 
electric  charges  in  the  same  way. 

In  the  electrolysis  of  hydrochloric  acid  the  cathion  material 
(H)  is  actually  set  free  at  the  cathode  and  the  anion  material 
(Cl)  is  actually  set  free  at  the  anode.  In  most  cases,  however, 
the  cathion  material  is  not  actually  set  free  at  the  cathode  nor 
is  the  anion  material  actually  set  free  at  the  anode.  Thus  in 
the  electrolysis  of  a  solution  of  sodium  chloride  (NaCl),  the 
cathion  material  (Na)  when  it  is  "liberated"  at  the  cathode 
immediately  reacts  with  the  water  forming  NaOH  and  free 
hydrogen;  in  the  electrolysis  of  a  solution'  of  copper  sulphate 
(CuSOJ  between  copper  electrodes,  the  anion  material  (864) 
combines  with  the  copper  of  the  anode  forming  fresh  CuSOi 
which  goes  into  solution,  or  it  is  deposited  as  crystals  on  the 
anode  if  the  solution  is  saturated;  in  the  electrolysis  of  H2SO4 
between  inert  electrodes,  the  hydrogen  is  set  free  at  the  cathode 
as  a  gas  and  the  anion  material  (SC^)  reacts  on  the  water  ac- 
cording to  the  formula  864  +  t^O  =  H2SO4  +  O,  and  the  free 
oxygen  escapes  as  a  gas. 

89.  Current  density  at  the  electrodes. — Generally  the  flow  of 
current  from  the  anode  plate  into  the  electrolyte  and  from  the 
electrolyte  into  the  cathode  plate  is  not  uniformly  distributed  over 
the  surfaces  of  the  plates.  There  is  always  a  tendency  for  the 
flow  of  current  to  be  concentrated  at  the  sharp  edges  of  the 
plates  and  at  any  sharp  projecting  part  of  the  plates.  Thus  Fig. 
115  represents  a  top  view  of  an  electrolytic  cell,  A  A  being  the 


ELECTROLYSIS   AND    BATTERIES. 


I87 


anode  and  CC  being  the  cathode,  and  the  fine  curved  lines  repre- 
sent the  stream  lines  of  the  electric  current  through  the  electro- 
lyte. The  crowding  together  of  the  stream  lines  at  the  corners 
of  the  electrodes  and  at  the  sharp  point  on  CC  represents  the  con- 
centration of  the  current-flow  at  these  places.  With  electrodes 
placed  as  shown  in  Fig.  115  there  is  extremely  little  flow  of 
current  into  or  out  of  the  back  faces  bb  bb  of  the  electrodes. 


glass  jar 


Fig.  115. 


When  the  electrodes  are  parallel  flat  plates  at  a  distance  apart 
which  is  small  as  compared  with  the  size  of  the  plates,  then  the 
flow  of  current  is  almost  wholly  confined  to  the  front  faces  ffffot 
the  electrodes  as  shown  in  Fig.  116,  the  flow  of  current,  further- 
more, is  distributed  over  the  faces  //  //  with  approximate  uni- 
formity, and  the  total  current  divided  by  the  area  of  one  of  the 
front  faces  //  is  called  the  current  density. 

The  current  density  at  an  electrode  has  a  great  deal  to  do  with 
the  character  of  the  chemical  action  at  the  electrode.  Thus,  if 
the  electrolyte  contains  zinc  sulphate  and  copper  sulphate,  copper 
only  is  deposited  on  the  cathode  if  the  current  density  is  low, 
but  both  copper  and  zinc  (and  also  some  hydrogen)  are  deposited 
on  the  cathode  if  the  current  density  is  large.  In  the  operation 
of  silver  plating  or  copper  plating  or  nickel  plating  the  deposited 
metal  is  soft  and  granular  if  the  current  density  is  too  high. 

90.  Definition  of  electrochemical  equivalent.  Chemical  cal- 
culations in  electrolysis. — The  amount  of  silver  deposited  per 


188 


ELECTRIC   LIGHTING. 


second  in  the  operation  of  silver  plating  is  proportional  to  the 
strength  of  the  current  in  amperes,  and  the  amount  of  silver 
deposited  in  one  second  by  one  ampere  is  called  the  electrochemical 
equivalent  of  silver;  it  is  equal  to  0.001118  gram  per  ampere- 
second  or  4.025  grams  per  ampere-hour. 

In  the  great  majority  of  cases  no  material  is  actually  deposited 
on  either  electrode  in  an  electrolytic  cell,  but  chemical  action  is 
always  produced  in  the  immediate  neighborhood  of  the  elec- 
trodes, and  it  is  important  to  consider  the  amount  of  chemical  action 
which  takes  place  in  a  given  time  due  to  the  flow  of  a  given  current 
through  the  cell.  A  general  statement  of  this  matter  involves 
the  use  of  a  number  of  chemical  terms.  These  terms  are  ex- 
hibited in  the  following  schedules. 

The  valencies  of  various  metals,  acid  radicals,  etc.,  are  shown 
by  the  numbers  in  the  following  exhibit  which  shows  the  chemical 
symbols  of  several  common  acids  and  salts. 

EXHIBIT   OF    VALENCIES. 


Name. 

Hydrochloric 
Acid. 

Silver  Nitrate. 

Njtric  Acid. 

Sulphuric  Acid. 

Chemical  symbol  
Valency  

H 
i 

Cl 
I 

Ag 
i 

N03 
i 

H 
i 

N03 

i 

Hf        SO, 

2               2 

Name. 

Cupric  Sulphate. 

Zinc  Sulphate. 

Aluminum 
Sulphate. 

Chemical  symbol 

Cu 

2 

SO4 

2 

Zn 

2 

SO4 

2 

A'. 

o 

(S04)3 
6 

Valency... 

The  chemical  equivalents  of  various  metals,  acid  radicals,  etc., 
are  shown  in  the  following  exhibit.  One  chemical  equivalent  of 
a  metal  or  acid  radical  is  hereafter  called  a  gram-val  of  the  sub- 
stance. 

EXHIBIT   OF   CHEMICAL   EQUIVALENTS   IN   GRAMS. 


Symbol  of  Substance. 

H 

Ag 

Cl 

N03 

S04 

Cu 

Zn 

Al 

Atomic  or  molecular 
weight. 

I  OI 

1  08 

5e.t 

62 

06 

63.6 

6iJ.4 

27.1 

Valency 

I 

I 

I 

I 

2 

2 

2 

T. 

Chemical  equivalent  in 
grams.  (The  gram- 
val)  

1.  01 

1  08 

35-5 

62 

48 

31-8 

32.7 

9-°3 

ELECTROLYSIS   AND   BATTERIES.  189 


The  number  of  grams  of  a  substance  in  one  gram-val  of  that 
stance  is  equal  to  the  atomic  or  molecular  weight  of  the  substance 
divided  by  the  valency  of  the  substance.  Thus  one  gram-val  of 
silver  is  108  grams  of  silver,  and  to  deposit  one  gram-val  of 
silver  on  the  cathode  in  a  silver  plating  cell  requires  96,540 
ampere-seconds  or  26.82  ampere-hours.  In  general,  96,540 
ampere  seconds  "  liberates  "  one  gram-val  of  anion  material  at 
the  anode  and  one  gram-val  of  cathion  material  at  the  cathode 
whatever  the  particular  electrolyte  may  be.  It  is  evident  there- 
fore that  96,540  ampere-seconds  is  an  important  unit  of  current  X 
time;  this  unit  is  called  the  faraday.  For  example  : 

One  faraday  (96,540  ampere-seconds)  "liberates" 
at  the  anode  at  the  cathode 

62  grams  of  NOs  from  nitric  acid  or  any  23    grams   of   Na   from   a   solution   oi 

nitrate  solution.  NaOH,  or  from  a  solution  of  any 

sodium  salt. 

48  grams  of  SO4  from  sulphuric  acid  or  31.8  grams  of  Cu  from  a  solution  of  any 

any  sulphate  solution.  cupric  salt. 

35.5  grams  of  Cl  from  hydrochloric  acid  63.6  grams  of  Cu  from  a  solution  of  any 

or  any  chloride  solution.  cuprous  salt.* 

16.01  grams  of  OH  from  a  solution  of  9.03  grams  of  Al  from  a  solution  of  any 

caustic  soda  or  potash,  etc.,  etc.  aluminum  salt,  etc.,  etc. 

91.  The  electrochemical  unit  of  work.  —  Consider  an  electro- 
lytic cell  through  which  a  current  of  I  amperes  is  flowing  and 
across  the  terminals  of  which  the  electromotive  force  is  E  volts. 
Work  is  being  delivered  to  the  cell  (done  on  the  cell)  at  the  rate 
El  watts,  and  in  /  seconds  the  amount  of  work  done  is  Elt 
joules.  f 

It  is  important  to  consider  the  amount  of  work  done  by  an 
electromotive  force  of  one  volt  during  the  flow  of  one  faraday 
(96,540  ampere-seconds)  through  a  cell.  This  amount  of  work 
may  be  conveniently  called  a  volt-faraday  ,  it  is  evidently  equal 
to  96,540  joules  and  it  is  therefore  equivalent  to  23,000  calories. 

*  Cupric  copper  has  a  valency  of  2,  cuprous  copper  has  a  valency  of  i.  Thus 
cupric  chloride  is  CuCh  and  cuprous  chloride  is  CuCl. 

f  It  takes  4.2  joules  to  raise  the  temperature  of  one  gram  of  water  i°  Centi- 
grade. That  is,  one  calorie  is  the  heat  equivalent  of  4.2  joules, 


190  ELECTRIC   LIGHTING. 

The  work  done  by  E  volts  during  the  flow  of  one  faraday  is 
E  volt-faradays,  or  96, 540 £  joules  and  it  is  equivalent  to 
23,oooJ3  calories. 

92.  Expenditure  of  work  in  electrolysis.    Heat  and  chemical 
work. — A  portion  of  the  work  done  in  forcing  a  current  through 
an  electrolytic  cell  is  converted  into  heat.     This  is  shown*  by 
the  fact  that  the  temperature  of  an  electrolytic  cell  rises  during 
the  flow  of  current.     Also  a  portion  of  the  work  done  in  forcing  a 
current  through  an  electrolytic  cell  is  left  tied  up,  as  it  were,  in 
the  chemical  changes  which  are  produced  by  the  current.     This 
work  which  becomes  tied  up  in  chemical  changes  is  called  chemical 
work.     Thus,  when  dilute  sulphuric  acid  is  electrolized  between 
electrodes  of  carbon  or  platinum,  hydrogen  and  oxygen  gases  are 
set  free,  and  it  is  evident  that  energy  is  tied  up  in  these  free  gases 
because  if  the  gases  are  re-combined  by  burning,  energy  is  ob- 
tained in  the  form  of  heat. 

The  amount  of  heat  developed  by  the  current  in  an  electro- 
lytic cell  depends  in  part  upon  the  resistancef  of  the  electrolyte 
in  ohms  and  it  depends  in  part  upon  irreversible  {  actions  at  the 
electrodes;  when  the  current  is  very  small  the  energy  which  is  lost 
as  heat  is  usually  negligible  in  comparison  with  the  energy  which 
becomes  tied  up  in  the  chemical  changes  which  are  brought  about 
by  the  current. 

93.  Decomposition  voltage. — Consider  the  electrolysis  of  dilute 
sulphuric  acid  between  inert  electrodes  of  carbon  or  platinum, 
the  current  being  so  small  that  the  loss  of  energy  in  the  production 
of  heat  is  negligible,  and  let   E  be  the  electromotive  force  across 

*  This  argument  is  not  strictly  correct  because  the  chemical  work  done  in  an 
electrolytic  cell  may  be  in  some  cases  greater  than  the  electrical  work  delivered  to 
the  cell,  the  cell  being  actually  cooled  in  the  process. 

t  The  matter  of  electrolyte  resistance  is  discussed  at  some  length  in  Whetham's 
Theory  of  Solution  and  in  H.  C.  Jones'  Physical  Chemistry, 

J  This  is  a  thermodynamic  term  which  the  beginner  is  not  expected  to  under- 
stand. See  two  papers  on  Reversible  and  Irreversible  Polarization  by  W.  S. 
Franklin  and  L.  A.  Freudenberger,  Transactions  of  the  American  Electrochemical 
Society,  Vol.  VII,  pages  33-49;  and  Vol.  VIII,  pages  227-237. 


ELECTROLYSIS   AND    BATTERIES.  191 

the  terminals  of  the  cell.  During  the  flow  of  one  fcraday  through 
the  cell  E  volt-faradays  of  work  will  be  done  on  the  cell,  and, 
heat  losses  being  negligible,  all  of  this  energy  will  be  tied  up  in 
the  i  .01  grams  of  free  hydrogen  and  the  8  grams  of  free  oxygen 
produced. 

Now  the  amount  of  energy  tied  up  in  these  gases  is  approxi- 
mately* equal  to  the  heat  of  combustion  of  i.oi  grams  of  hydro- 
gen, and  the  heat  of  combustion  of  hydrogen  is  34,700  calories 
per  gram.  Therefore  the  setting  free  of  i.oi  grams  of  H  and 
8  grams  of  0  involves  the  tying  up  of  the  energy  equivalent  of 
35,000  calories,  which  is  147,000  joules  or  1 .52  volt-faradays,  and 
this  must  be  equal  to  the  work  done  on  the  cell,  namely,  E 
volt-faradays.  Therefore  we  have 

E  volt-faradays  =  1.52  volt-faradays 

and  consequently  E,  which  is  the  voltage  required  to  send  a  very 
small  current  through  the  given  electrolytic  cell,  is  equal  to  1.52  volts, 
and  it  is  called  the  decomposition  voltage  of  sulphuric  acid. 

The  decomposition  voltages  of  some  common  acids  and  salts 
between  inert  electrodes  are  given  in  the  following  table: 

DECOMPOSITION  VOLTAGES,  f 
(For  Normal  Solutions.) 

Sulphuric  acid 1.67  volts.  Barium  nitrate 2.25  volts. 

Nitric  acid 1.69  volts.  Sodium  nitrate 2.15  volts. 

Hydrochloric  acid ....  1.31  volts.  Calcium  chloride 1.89  volts. 

Oxalic  acid 0.75  volts.  Potassium  chloride.  .  .  1.96  volts. 

Sodium  hydroxide ....  i  .69  volts.  Sodium  chloride 1.98  volts. 

Qualifications  of  Above  Statements  Concerning  Decomposition  Voltages. — 
The  above  statements  concerning  decomposition  voltages  are  not  in  accord  with 
experiment  in  the  following  particulars: 

*  The  heat  of  combustion  includes  the  heat  of  condensation  of  the  water  vapor 
produced  by  the  combustion,  but  a  small  amount  of  available  energy  is  represented 
by  the  placing  of  the  condensed  water  back  into  the  acid  solution.  This  small 
amount  of  energy  is  neglected. 

t  As  determined  by  observation  by  LeBlanc,  Zeitschrift  filr  Physikalische 
Chemie,  Vol.  VIII,  page  299,  1891.  One  must  not  be  surprised  at  the  discrepancy 
between  the  value  1.52  volts  above  calculated  and  the  value  1.67  volts  as  observed 
by  LeBlanc  for  dilute  sulphuric  acid.  See  page  192. 


192 


ELECTRIC   LIGHTING. 


(a)  A  very  small  current  through  sulphuric  acid  between  inert  electrodes  does 
not  set  free  hydrogen  and  oxygen  gases.  A  trace  of  oxygen  is  dissolved  in  the 
solution  and  it  combines  with  the  hydrogen  as  it  is  "liberated"  at  the  cathode, 
and  the  supply  of  dissolved  oxygen  is  replenished  by  diffusion  from  the  neighbor- 
hood of  the  anode.  Also  a  trace  of  hydrogen  is  dissolved  in  the  solution  and  it 
combines  with  the  oxygen  as  it  is  "liberated"  at  the  anode,  and  the  supply  of  dis- 
solved hydrogen  is  replenished  by  diffusion  from  the  neighborhood  of  the  cathode. 
Any  voltage,  however  small,  can  maintain  a  very  small  current  through  sulphuric 
acid  between  inert  electrodes,  and  the  same  is  true  of  any  electrolyte  whatever. 
There  is,  however,  a  definite  voltage  below  which  no  oxygen  and  hydrogen  gases 
are  set  free,  and  this  is  the  decomposition  voltage  above  referred  to.  Similarly, 
there  is  a  definite  decomposition  voltage  for  any  electrolyte  between  inert  electrodes. 

(5)  The  setting  free  of  oxygen  and  hydrogen  gases  at  a  rate  which  is  actually 
perceptible,  by  electrolizing  sulphuric  acid  between  inert  electrodes,  requires  about 
1.67  volts.  Therefore  1.67  volt-faradays  of  work  is  done  on  the  cell  during  the 
flow  of  one  faraday  through  the  cell,  1.52  volt-faradays  of  this  work  is  tied  up  in 
the  free  oxygen  and  hydrogen  gases,  and  the  remainder,  namely,  0.15  volt-faraday, 
is  converted  into  heat  at  the  electrodes  because  of  irreversible  actions  at  the  elec- 
trodes. That  is  to  say,  the  heat  generated  in  an  electrolytic  cell  does  not  always 
become  negligible  as  the  current  approaches  zero.  The  heat  generated  in  the  body 
of  the  electrolyte  because  of  the  resistance  of  the  electrolyte  (in  ohms)  does  become 
negligible. 

(c)  The  application  of  thermodynamics  to  electrolysis  shows  that  it  is  pos- 
sible for  the  "chemical  work"  done  in  an  electrolytic  cell  to  exceed  the  electrical 
work  done  on  the  cell,  the  deficiency  being  made  up  by  the  cooling  of  the  cell.  In 
such  a  case  the  "decomposition  voltage"  would  be  less 'than  what  is  calculated  by 
the  theory  above  outlined. 

94.  Electrode  polarization. — When  a  metal  plate  is  allowed  to  stand  in  an  acid 
or  salt  solution  a  definite  potential-difference  or  voltage  comes  into  existence  be- 
tween the  solution  and  the  metal.  This  potential-difference  or  voltage  measures 
what  is  called  the  electrode  polarization.  Thus,  according  to  Neumann*  the 
values  of  electrode  polarization  between  ordinary  metals  and  solutions  of  their 
salts  are  as  follows,  the  voltage  being  reckoned  as  positive  -when  it  is  from  the  solution  to 
the  metal: 

ELECTRODE   POLARIZATION   VOLTAGES. 
(Equilibrium  Values  in  Volts.) 


Metal 

Salt  of  Metal. 

Sulphate. 

Nitrate. 

Chloride. 

Zinc 

—  O  ^24, 

—  O  4.77 

—  O  ^O7 

Iron 

—  O  OO"? 

—  o  087 

Lead 

-i-O  1  1  c 

-j-o  005 

Copper 

4-o  ej  t 

-f~o  615 

*  Zeitschrift  fitr  physikalische  Chemie,  Vol.  XIV,  page  229,  1894. 


ELECTROLYSIS    AND    BATTERIES. 


193 


The  polarization  voltages  given  in  this  table  are  equilibrium  values,  that  is, 
the  values  which  exist  when  no  current  flows  from  metal  to  electrolyte  or  from 
electrolyte  to  metal.  When  there  is  a  flow  of  current  the  polarization  voltage 
.changes  considerably.  TMs  change  is  due  chiefly  to  the  change  of  concentration 
of  the  electrolyte  which  always  takes  place  near  an  electrode  as  explained  in  con- 
nection with  the  lead  storage  battery  in  Art.  105.* 

wire 


zinc  plate 

—ZnS04 
solution 


-CuSOj. 
solution 


copper 
plate 


Fig.  117. 


Fig.  118. 


One  might  think  that  the  polarization  voltage  between  a  solution  and  a  metal 
plate  P  could  be  measured  by  connecting  a  voltmeter  as  shown  in  Fig.  117,  but 
there  is  a  polarization  voltage  between  the  solution  and  the  wire  W  so  that  the 
voltmeter  would  measure  the  sum: 

volts  from  wire   W  to  solution  +  volts  from  solution  to  plate  P, 
or  the  difference 

—  volts  from  solution  to  wire    W    +  volts  from  solution  to  plate   P. 

The  measurement  of  the  polarization  voltage  between  the  metal  plate  P  and  a 
solution  depends  upon  the  use  at  W  of  an  electrode  -whose  polarization  voltage  has  been 
determined.^  Such  an  electrode  is  called  a  standard  electrode. 

Example. — Consider  the  electrolytic  cell  which  is  shown  in  Fig.  118,  in  which  the 
zinc  sulphate  solution  floats  on  the  heavier  copper  sulphate  solution.  Neglecting 
the  voltage  across  the  contact  cc  of  the  solutions,  the  voltage  indicated  by  the 
voltmeter  V  is  the  sum: 

volts  from  zinc  to  solution  +  volts  from  solution  to  copper, 

*  Another  cause  of  change  of  polarization  voltage  with  current  is  discussed  in 
two  papers  on  Reversible  and  Irreversible  Polarization  by  W.  S.  Franklin  and  L.  A. 
Freudenberger  which  are  referred  to  on  page  190. 

t  Two  methods  have  been  employed  for  measuring  the  polarization  voltage  of 
the  standard  electrode.  This  matter  is  fully  discussed  in  Whetham's  Theory  of 
Solution,  Chapter  XI,  Cambridge  University  Press,  1902. 


194  ELECTRIC   LIGHTING 

or  the  difference 

—  volts  from  solution  to  zinc  +  volts  from  solution  to  copper. 

According  to  the  above  table,  voltage  from  solution  to  zinc  is  —  0.524,  and  voltage 
from  solution  to  copper  is  +  0.515,  so  that  the  voltage  indicated  by  the  voltmeter 
would  be  1.039.  This  voltage  depends  upon  the  degree  of  concentration  of  the 
solutions.  With  a  concentrated  solution  of  copper  sulphate  and  a  fairly  dilute 
solution  of  zinc  sulphate  the  voltmeter  would  indicate  about  1.08  volts. 

Calculation  of  electrode  polarization. — The  total  voltage  (the  decomposition 
voltage)  required  to  force  an  infinitesimal  current  through  an  electrolytic  cell  may 
be  calculated  from  the  chemical  work  as  explained  in  Art.  93;  and  if  one  could 
determine  the  portion  of  the  chemical  work  which  is  done  at  the  anode  and  the 
portion  which  is  done  at  the  cathode  then  the  total  decomposition  voltage  could  be 
divided  into  two  known  parts,  and  these  parts  would  be  the  anode  polarization  and 
the  cathode  polarization  respectively.  There  is,  however,  no  chemical  data  in 
existence  upon  which  such  a  calculation  can  be  based,  and  even  if  such  chemical 
data  did  exist  the  results  would  be  subject  to  the  qualifications  outlined  in  the  fine 
print  in  Art.  93. 

95.  The  voltaic  cell.* — The  chemical  action  produced  by  the 
flow  of  current  through  an  electrolytic  cell  is  confined  wholly 
to  the  immediate  neighborhood  of  the  electrodes,  and  this  chem- 
ical action  is  usually  forced,  that  is,  work  has  been  done  to  bring 
it  about,  or,  in  other  words,  an  outside  electromotive  force  is  re- 
quired to  push  the  current  through  the  cell.  But  in  many  cases 
the  chemical  action  produced  by  the  flow  of  current  through  an 
electrolytic  cell  is  a  source  of  energy.  In  such  a  case  the  electro- 
lytic cell  itself  can  maintain  a  current  through  the  electrolyte 
from  electrode  to  electrode  and  through  an  outside  circuit  of 
wire  which  connects  the  electrodes.  Such  an  electrolytic  cell  is 
called  a  voltaic  cell  or  primary  battery. 

Example. — When  a  strip  of  clean  zinc  and  a  strip  of  copper  or 
carbon  are  dipped  into  dilute  sulphuric  acid,  no  chemical  action 
takes  place.  But  when  the  plates  are  connected  together  by  a 
wire,  a  current  immediately  starts  to  flow  through  the  circuit, 
leaving  the  cell  at  the  copper  or  carbon  electrode  (the  cathode) 
and  entering  the  cell  at  the  zinc  electrode  (the  anode).  This 
current  decomposes  the  sulphuric  acid  (H2SO4),  the  hydrogen  is 

*  A  number  of  voltaic  cells  connected  together  constitute  a  voltaic  battery. 
The  word  battery  is,  however,  frequently  applied  to  a  single  cell. 


ELECTROLYSIS   AND   BATTERIES.  195 

set  free  at  the  copper  or  carbon  cathode  and  escapes  from  the  cell 
as  a  gas,  and  the  sulphuric  acid  radical  (SO4)  which  is  "liberated" 
at  the  zinc  anode  combines  with  the  zinc  and  forms  zinc  sulphate 
(ZnSO4)  which  goes  into  solution.  The  combination  of  Zn  and 
SO4  develops  more  energy  than  is  required  for  the  decomposition 
of  the  H2SO4  so  that  the  chemical  action  in  this  cell  is  a  source  of 
energy.  The  cell  here  described  is  called  the  simple  voltaic  cell. 

96.  Electromotive  force  of  a  voltaic  cell.  —  A  clear  idea  of  the 
electromotive  of  a  voltaic  cell  may  be  obtained  by  the  following 
argument  :  (a)  The  amount  of  chemical  action  which  takes  place 
in  a  given  voltaic  cell  is  proportional  to  7  X  t,  where  /  is  the 
current  and  /  is  the  time  during  which  the  current  continues 
to  flow,  as  explained  in  Art.  90.  Furthermore  the  energy  evolved 
by  the  chemical  action  is  proportional  to  the  amount  of  chemical 
action;  therefore  the  energy  evolved  by  the  chemical  action  is 
proportional  to  I  X  t  and  it  can  be  expressed  as  elt  where  e  is 
a  constant  for  a  given  type  of  voltaic  cell. 

(6)  The  energy  delivered  to  an  electric  circuit  is  equal  to 
RPt  joules,  where  R  is  the  resistance  of  the  circuit  in  ohms,  / 
is  the  current  in  amperes,  and  /  is  the  elapsed  time  in  seconds. 

(c)  If  all  of  the  energy  of  the  chemical  action  were  available  for 
the  maintenance  of  the  current  then  elt  (the  energy  used  to  main- 
tain the  current)  would  be  equal  to  RPt  (the  energy  which  ap- 
pears in  the  electric  circuit)  .  That  is  : 

elt  =  RPt 
or 


Or,  in  words,  the  current  produced  by  the  given  voltaic  cell  in  a 
circuit  of  resistance  I  is  equal  to  the  factor  e  [as  denned  under 
(a)]  divided  by  R.  Now  this  relation  is  what  is  familiarly  known 
as  Ohm's  law  and  the  factor  e  is  the  electromotive  force  of  the 
given  voltaic  cell. 

The  electromotive  force  of  a  voltaic  cell  is  entirely  independent 


196  ELECTRIC    LIGHTING. 

of  the  size  of  the  cell,  it  depends  only  on  the  character  of  the 
chemical  action  in  the  cell. 

The  electromotive  force  of  a  voltaic  cell  is  most  easily  measured 
by  connecting  a  voltmeter  to  the  terminals  of  the  cell. 

The  above  argument  may  well  be  repeated  as  applied  to  a 
particular  case,  (a)  Consider  the  energy  evolved  by  the  dis- 
solution of  the  zinc  in  the  simple  voltaic  cell  which  is  described 
in  Art.  95.  The  net  result  of  the  chemical  action  in  this  cell  is 
represented  by  the  formula 

Zn  +  H2SO4  =  ZnSO4  +  H2. 

During  the  flow  of  one  faraday  through  such  a  cell  one  gram-val 
(32.7  grams)  of  zinc  would  be  dissolved  and  a  corresponding 
amount  of  hydrogen  would  be  set  free.  Now  the  dissolution  of 
one  gram  of  zinc  in  dilute  sulphuric  acid  develops  578  calories 
of  heat  which  is  the  equivalent  of  2428  joules  or  0.822  volt- 
faradays  of  work. 

(b)  Let  E  be  the  electromotive  force  of  the  cell.     Then  during 
the  flow  of  one  faraday  the  cell  would  deliver    E   volt-faradays 
of  electrical  work. 

(c)  If  all  the  energy  evolved  by  the  dissolution  of  the  zinc  in 
the  simple  voltaic  cell  were  available  in  the  form  of  electrical- 
energy  output  then,  from  (a)  and  (b)  we  would  have 

E  volt-faradays  =  0.822  volt-faradays 
or 

E  =  0.822  volts. 

(d)  As  a  matter  of  fact  the  electromotive  force  of  the  simple 
voltaic  cell  under  discussion  is  1.03  volts  on  open  circuit  and  it 
falls  off  very  greatly  when  the  cell  delivers  current. 

97.  Polarization  of  a  voltaic  cell. — The  electromotive  force 
between  the  terminals  of  a  voltaic  cell  is  always  less  when  the 
cell  is  delivering  current  than  it  is  when  the  cell  is  not  delivering 
current.  This  difference  is  at  first  due  chiefly  to  the  loss  of 
voltage  due  to  the  resistance  of  the  cell.  Thus  a  voltaic  cell  has 


ELECTROLYSIS   AND   BATTERIES.  197 

an  "open-circuit"  electromotive  force  of  2  volts  and  an  internal 
resistance  of  0.05  ohm,  and  the  electromotive  force  between  the 
terminals  of  the  cell  drops  instantly  to  1.5  volts  when  the  cell 
is  called  upon  to  deliver  10  amperes.  The  loss  of  voltage  due 
to  internal  resistance  is  in  this  case  0.5  volt  and  it  is  equal  to 
the  current  of  10  amperes  multiplied  by  the  internal  resistance 
of  0.05  ohm. 

When  a  voltaic  cell  continues  to  deliver  current  the  electro- 
motive force  between  the  terminals  of  the  cell  falls  off  more  and 
more.  This  falling  off  of  the  electromotive  force  of  a  voltaic 
cell  is  called  polarization.*  The  chief  cause  of  the  polarization 
of  a  voltaic  cell  is  as  follows:  The  chemical  action  in  the  neighbor- 
hood of  the  electrodes  brings  about  local  changes  of  composition 
and  of  concentration  of  the  electrolyte,  less  energy  is  evolved  by 
the  chemical  action  at  the  electrodes,  and  consequently  the 
voltage  of  the  cell  decreases. 

98.  The  bichromate  cell. —  The  available  energy  of  the  chemical 
action  which  takes  place  in  the  simple  voltaic  cell  which  is  described 
as  an  example  in  Art.  p$  may  be  greatly  increased  by  providing  an 
oxidizing  agent  in  the  neighborhood  of  the  cathode  so  that  the  hydrogen 
may  be  oxidized  at  the  moment  of  its  "liberation"  by  the  current. 
The  increase  of  available  energy  because  of  this  oxidation  gives  a 
greatly  increased  voltage.  An  oxidizing  agent  used  in  this  way 
is  called  a  depolarizer,  f  The  bichromate  cell  furnishes  a  good 
example  of  the  use  of  an  oxidizing  agent  in  a  voltaic  cell. 

The  simplest  form  of  bichromate  cell,  which  is  sometimes 
called  the  Grenet  cell  from  its  inventor,  is  shown  in  section  in 
Fig.  1 19  a.  The  electrodes  are  a  carbon  plate  C  and  an 
amalgamated  J  zinc  plate  Z,  and  the  electrolyte  e  e  e  is  dilute 

*  This  term  must  not  be  confused  with  the  term  electrode  polarization  as  defined 
in  Art.  94. 

t  In  the  whole  history  of  physics  words  without  meanings  have  been  used  for 
things  not  understood.  Thus  the  word  polarize  does  a  great  variety  of  questionable 
duty  in  the  subject  of  electrolysis  in  the  same  way  that  the  word  induce  does  a 
great  variety  of  questionable  duty  in  electromagnetism !  It  would  be  a  great 
help  if  all  such  words  could  be  thrown  away. 

t  Covered  with  a  thin  coating  of  mercury. 


198 


ELECTRIC    LIGHTING. 


sulphuric  acid  in  which  potassium  bichromate  or  chromic  acid 
has  been  dissolved.  Without  the  potassium  bichromate  the 
hydrogen  escapes  as  a  gas  and  the  voltage  of  the  cell  is  1.03; 
with  the  bichromate  the  hydrogen  is  oxidized  and  the  voltage  of 
the  cell  is  1.90.  There  is  a  very  rapid  waste  of  zinc  (and  acid) 
in  this  cell  and  the  cell  is  now  seldom  used. 


wire 


wire 


= 

c 

Z 

? 

•*-  g  lass 

~  -  -=~  —  "• 

e 

jar 

e 

c 

e 

Z 

Fig.  119  a. 


Fig.  119&. 


A  modified  form  of  bichromate  cell,  known  as  the  Fuller  cell, 
is  shown  in  section  in  Fig.  1196.  In  this  cell  the  electrolyte  is 
dilute  sulphuric  acid  but  the  zinc  anode  is  contained  in  a  porous 
earthenware  cup  and  the  potassium  bichromate  or  chromic  acid 
is  dissolved  only  in  that  portion  of  the  electrolyte  which  surrounds 
the  carbon  cathode.  There  is  not  a  rapid  waste  of  zinc  (and 
acid)  in  this  cell  and  the  cell  is  extensively  used. 

99.  Voltaic  action  and  local  action. — Two  kinds  of  chemical 
action  are  to  be  distinguished  in  a  voltaic  cell :  (a)  the  chemical 
action  which  depends  upon  the  flow  of  current,  and  does  not 
take  place  when  there  is  no  current;  and  (b)  the  chemical  action 
which  is  independent  of  the  flow  of  current,  and  which  does  take 
place  whether  the  current  is  flowing  or  not. 

The  chemical  action  which  depends  on  the  current  is  propor- 
tional to  the  current,  it  is  essential  to  the  operation  of  the  voltaic 


ELECTROLYSIS   AND   BATTERIES.  199 

cell  as  a  generator  of  current,  its  energy  is  available  for  the 
maintenance  of  the  current,  and  it  is  called  voltaic  action. 

The  chemical  action  in  a  voltaic  cell  which  is  independent  of 
the  flow  of  current  does  not  help  in  any  way  to  maintain  the 
current,  it  represents  absolute  waste  of  materials,  and  it  is  called 
local  action. 

Local  action  takes  place  more  or  less  in  every  type  of  voltaic 
cell  and  it  is  especially  great  in  the  Grenet  cell  where  the  oxidizing 
agent  comes  into  contact  with  the  zinc  plate.  Local  action  is 
greatly  reduced  by  coating  the  zinc  plate  with  a  thin  coating  of 
metallic  mercury  and  by  using  very  pure  zinc. 

The  amount  of  zinc  usefully  consumed  by  voltaic  action  while 
a  voltaic  cell  in  delivering  a  given  current  for  a  specified  time, 
is  equal  to  the  amount  of  zinc  that  would  be  deposited  by  the 
given  current  during  the  specified  time  upon  the  cathode  of  an 
auxiliary  electrolytic  cell  containing  a  solution  of  a  zinc  salt. 
For  example  five  amperes  flowing  for  one  hour  will  deposit  6.1 
grams  of  zinc,  and  therefore  6.1  grams  of  zinc  (and  a  correspond- 
ing amount  of  acid  and  bichromate)  are  usefully  consumed  in  a 
Grenet  cell  in  the  delivery  of  5  amperes  for  one  hour.  In  an 
actual  test  of  a  Grenet  cell  delivering  5  amperes  for  one  hour  the 
loss  of  zinc  was  30  grams.  Under  the  conditions  of  the  test, 
therefore,  23.9  grams  of  zinc  (and  a  corresponding  amount  of 
acid  and  bichromate)  were  wasted  by  local  action  and  6.1  grams 
of  zinc  (and  a  corresponding  amount  of  acid  and  bichromate) 
were  usefully  consumed. 

100.  Open-circuit  cells  and  closed-circuit  cells. — A  voltaic  cell 
which  can  be  left  standing  unused  but  in  readiness  at  any  time 
for  the  delivery  of  current  when  its  circuit  is  closed  is  called  an 
open-circuit  cell.  An  open-circuit  cell  must,  above  all  things,  be 
nearly  free  from  local  action.  The  cell  most  extensively  used 
for  open-circuit  service  is  the  LeClanche*  cell  which  is  described 
as  the  manganese-dioxide  cell  in  Art.  103. 

A  voltaic  cell  which  is  suitable  for  delivering  a  current  steadily 
is  called  a  closed-circuit  cell.  A  closed-circuit  cell  should  be  of  a 


200  ELECTRIC   LIGHTING. 

type  of  which  the  voltage  does  not  fall  off  greatly  with  continued 
delivery  of  current,  and,  of  course,  local  action  should  be  elimi- 
nated if  possible.  The  gravity  Daniell  cell,  the  Fuller  cell,  the 
copper  oxide  cell,  and  the  lead  storage  cell  are  most  extensively 
used  for  closed  circuit  work. 

101.  The  gravity  Daniell  cell. — The  essential  features  of  the 
gravity  Daniell  cell  are  shown  in  Fig.  118.     The  usual  form  of 

the  cell  is  shown  in  Fig.  120.  During  the 
operation  of  the  cell  metallic  copper  is 
deposited  upon  the  copper  cathode  at 
the  bottom  of  the  cell,  and  the  SO±  com- 
bines with  the  zinc  of  the  anode,  form- 
ing ZnSCV  The  electromotive  force  of 
this  cell  varies  from  about  1 .05  volts  to 
i.io  volts,  depending  upon  the  degree  of 
concentration  of  the  zinc  sulphate  and 
copper  sulphate  solutions. 

This  cell  has  a  considerable  amount  of  local  action  when  it  is 
allowed  to  stand  unused  because  of  the  upward  diffusion  of  the 
copper  sulphate.  It  is  used  very  extensively  in  telegraphy  and 
for  operating  the  "track  circuit"  relays  in  automatic  railway 
signalling. 

1 02.  The  copper-oxide  cell. — In  this  type  of  cell  the  anode  is 
zinc,  the  electrolyte  is  a  solution  of  caustic  soda,  and  the  cathode 
is  a  highly  compressed  block  of  copper  oxide.     The  flow  of 
current  through  the  cell  "liberates"  Na  at  the  cathode  and  OH 
at  the  zinc  anode  and  the  following  reactions  take  place : 

At  the  cathode  Na    +  i(CllO)  +  J(H2O)   =  JCll  +  NaOH 
T  direction  of  flow  of  current  through  the  cell. 

At  the  anode  OH  +     |Zn     +  NaOH  =  |(Na2ZnO2)  +  H2O. 

The  atomic  weights  (or  molecular  weights)  of  the  various 
substances  in  this  schedule,  multiplied  by  the  factor  J  or  not  as 
the  case  may  be,  express  the  number  of  grams  of  the  various 


ELECTROLYSIS   AND    BATTERIES.  2OI 

substances  involved  in  the  chemical  action  produced  by  the  flow 
of  one  faraday  through  the  cell.* 

The  copper-oxide  cell  has  but  little  local  action  and  its  electro- 
motive force  is  about  0.6  volt.  This  cell  is  used  extensively  for 
operating  railway  signals;  that  is  for  operating  the  small  motors 
which  move  the  signal  arms.  The  track  relays  are  usually 
operated  by  gravity  cells. 

103.  The  manganese-dioxide  cell. — In  this  cell  the  anode  is 
zinc,  the  electrolyte  is  a  solution  of  ammonium  chloride  (sal 
ammoniac)  and  the  cathode  is  a  plate  of  carbon  with  bits  of 
coke  and  manganese  dioxide  packed  closely  around  it.  The 
earliest  cell  of  this  type  is  called  the  LeClanche  cell  from  its 
inventor,  and  in  this  cell  the  manganese  dioxide  and  coke  are 
contained  in  a  porous  earthenware  cup.  The  ordinary  dry  cell\ 
is  a  manganese-dioxide  cell  in  which  the  containing  vessel  is 
made  of  sheet  zinc  and  it  serves  as  the  anode,  the  electrolyte  is 
held  in  a  porous  mass  of  saw-dust  or  other  absorbent  material, 
and  several  thicknesses  of  unglazed  paper  keep  the  manganese 
dioxide  and  powdered  coke  away  from  the  zinc. 

The  flow  of  current  through  the  manganese-dioxide  cell  "liber- 
ates" chlorine  at  the  zinc  anode  and  NH4  at  the  carbon  cathode 
and  the  following  reactions  take  place : 

At  the  cathode  NH4  +  i(MnO2)  =  NH3  +  i(HiO)  +  |(MnO) 

Direction  of  current  through  the  cell. 
At  the  anode    Cl       +        JZn         =  J(ZnCl2) 

There  is  but  little  local  action  in  the  manganese-dioxide  cell  if 
the  zinc  and  ammonium  chloride  are  pure,  J  but  the  cell  polarizes 
rapidly  when  it  delivers  steady  current.  Reliable  manufacturers 

*  This  statement  applies  also  to  the  reaction  schedules  given  on  pages  204,  205 
and  206. 

f  The  dry  cell  has  been  denned  as  a  cell  which  being  sealed  is  always  wet,  whereas 
the  wet  cell  being  open  to  the  air  often  becomes  dry. 

J  See  important  papers  on  the  dry  cell,  Transactions  of  the  American  Electro- 
chemical Society,  Vol.  XVI,  pages  97  and  109;  Vol.  XVII,  page  341;  and  Vol.  XIX, 
page  31. 


202  ELECTRIC   LIGHTING. 

always  stamp  the  date  of  manufacture  on  their  dry  cells,  and  the 
purchaser  should  not  accept  a  cell  which  is  more  than  two  or  three 
months  old.  The  best  test  of  a  dry  cell  is  to  observe  the  short- 
circuit  current  by  connecting  the  cell  momentarily  to  an  ammeter. 
A  fresh  cell  2\  inches  in  diameter  and  6  inches  high  should  give 
at  ordinary  room  temperature  about  20  amperes  short-circuit 
current.  The  electromotive  force  of  the  manganese-dioxide  cell 
is  about  1 .6  volts. 

104.  Regeneration  of  a  voltaic  cell  by  a  reversed  current. — 

An  essential  feature  of  voltaic  action  is  that  it  is  reversed  if  a 
current  is  forced  backwards  through  a  voltaic  cell  by  an  outside  agent, 
provided  that  no  material  that  has  played  a  part  in  the  previous 
voltaic  action  has  been  allowed  to  escape  from  the  cell.  Thus, 
in  the  operation  of  the  simple  voltaic  cell  consisting  of  a  zinc 
anode  and  carbon  cathode  in  dilute  sulphuric  acid,  the  H2SO4 
is  decomposed,  ZnSC>4  is  formed  at  the  anode,  and  hydrogen  is 
liberated  at  the  cathode.  If  the  current  is  reversed  so  that  the 
carbon  plate  becomes  the  anode  and  the  zinc  plate  the  cathode, 
then  the  ZnSCX  previously  formed  will  be  decomposed,  metallic 
zinc  will  be  deposited  upon  the  zinc  cathode,  and  SO*  will  be 
liberated  at  the  carbon  anode  where  it  will  combine  with  the 
trace  of  hydrogen  that  is  clinging  to  the  carbon  plate  and  form 
H2SO4.  In  this  cell  the  greater  part  of  the  liberated  hydrogen 
has  of  course  escaped  and  the  reversed  chemical  action,  due  to  a 
reversed  current  cannot  long  continue.  Local  action,  on  the 
other  hand,  being  independent  of  current,  is  not  affected  by  a  reversal 
of  the  current. 

The  storage  cell. — A  voltaic  cell  which  is  free  from  local  action 
and  in  which  all  of  the  materials  which  take  part  in  the  voltaic  action 
are  kept  in  the  cell,  may  be  regenerated  after  use  by  sending  through 
it  a  reversed  current.  This  regeneration  is  due  to  the  reversed 
chemical  action  that  is  produced  by  the  reversed  current,  as 
explained  above.  A  voltaic  cell  which  can  be  thus  regenerated 


ELECTROLYSIS   AND    BATTERIES. 


203 


is  called    a  storage  cell.     The  process  of  regeneration  is  called 
and  the  use  of  the  cell  as  an  electric  generator  is  called 


discharging.  4 

The  capacity  of  a  storage  cell  is  expressed  in  ampere-hours. 
Thus  a  cell  which  can  deliver  10  amperes  for  8  hours  is  said 
to  have  a  capacity  of  80  ampere-hours. 

The  electrode  out  of  which  current  flows  while  a  storage  cell 
is  discharging  is  called  the  positive  electrode,  and  the  other 
electrode  is  called  the  negative  electrode.  This  matter  can  be 

positive  main 


positive 
grid 


D  C  supply  mains 


negative  main 


negative 
grid 


rheostat 


Fig.  121. 


positive 
grid 


Fig.  122. 


most  easily  remembered  with  the  help  of  diagrams.  Thus  Fig. 
121  shows  a  storage  cell  discharging,  and  Fig.  122  shows  a 
storage  cell  being  charged. 

Almost  any  kind  of  voltaic  cell  can  be  used  to  some  extent 
as  a  storage  cell,  that  is  to  say,  almost  any  kind  of  voltaic  cell 
can  be  regenerated  to  some  extent  by  forcing  a  reversed  current 
through  it,  but  a  good  storage  cell  must  be  free  from  local  action, 
and  the  materials  which  take  part  in  the  voltaic  action  must 
be  kept  in  the  cell,  as  pointed  out  above;  and  the  electrodes 
must  not  crumble  to  pieces  with  frequent  charging  and  discharg- 
ing of  the  cell.  The  only  voltaic  cells  which,  up  to  the  present 


204  ELECTRIC    LIGHTING. 

time,   have   been   found   to   meet   these   requirements  are   the 
lead  cell*  and   the  nickel-iron  cell.f 

105.  The  lead  storage  cell. — When  thelead  cell  is  fully  charged 
it  has  a  positive  electrode  of  lead  peroxide  (PbO2),  a  negative 
electrode  of  spongy  metallic  lead  (Pb),  and  an  electrolyte  of 
dilute  sulphuric  acid  (H2SO4).  When  the  cell  discharges  the 
lead  peroxide  is  reduced  to  lead  oxide  (PbO)  which  absorbs  sul- 
phuric acid  from  the  solution  and  is  converted  into  insoluble  lead 
sulphate  (PbS04),  and  the  spongy  metallic  lead  is  oxidized  and 
similarly  converted  into  insoluble  lead  sulphate. 

The  lead  peroxide  and  the  spongy  metallic  lead  (or  the  insoluble 
lead  sulphate  into  which  these  materials  are  converted  by  dis- 
charge) constitute  the  active  electrode  materials  of  the  lead  cell. 
These  active  materials  are  held  in  grooves  or  pockets,  in  plates 
or  grids  of  solid  metallic  lead. 

The  chemical  actions  which  take  place  in  the  charging  and 
discharging  of  the  lead  storage  cell  are  shown  in  the  following 
schedule : 

DISCHARGING. 
Positive  grid      H  +$  (PbO2)  +  |(H2SO4)  =  H2O  +  £(PbSO4) 

I     Direction  of  current  through  the  cell 
Negative  grid  |(SO4)  +   ^Pb  =  £(PbSO4) 

CHARGING. 
Positive  grid  |(SO4)  +  |(PbSO4)  +  H2O  =  H2SO4  +  £(PbO«) 

T    Direction  of  current  through  the  cell. 
Negative  grid     H  +  ^(PtfSOO  =  i(H2SO4)  +  |Pb 

Effects  of  charge  and  discharge. — The  conversion  of  the  PbO2 
and  the  Pb  into  PbSO4  on  discharge  causes  a  great  decrease  in 
the  concentration  of  the  electrolyte,  especially  in  the  pores  of 
the  active  material,  and  an  increase  of  volume  of  the  active 

*  The  details  of  construction  of  the  lead  storage  cell  are  very  fully  described 
on  pages  147-200  of  Lyndon's  Storage  Battery  Engineering,  McGraw-Hill  Book  Co., 
1911. 

t  Sometimes  called  the  Edison  cell.  The  earlier  type  off  nickel-iron  storage 
cell  is  described  by  A.  E.  Kennally,  Transactions  of  the  American  Institute  of 
Electrical  Engineers,  Vol.  XVIII,  pages  219-244,  May,  1901. 


ELECTROLYSIS   ARD    BATTERIES.  205 


electrode  materials.  The  reconversion  of  the  PbSOi  into 
and  Pb  by  charging  causes  a  corresponding  increase  in  the  con- 
centration of  the  electrolyte  and  a  decrease  of  volume  of  the 
active  electrode  materials. 

The  changes  of  concentration  of  the  electrolyte  are  the  chief 
causes*  of  the  decrease  of  voltage  of  the  cell  during  discharge 
and  of  the  increase  of  voltage  of  the  cell  while  it  is  being  charged 
(see  Fig.  123). 

The  expansion  and  contraction  of  the  active  electrode  materials 
is  the  chief  cause  of  the  disintegration  of  the  electrodes,  and  it 
also  tends  to  cause  the  plates  or  grids  to  buckle  or  warp,  especially 
if  the  action  is  not  the  same  on  both  sides  of  a  plate.  A  well- 
designed  storage  battery  grid  allows  the  active  electrode  material 
to  expand  and  contract  with  a  minimum  of  mechanical  damage 
to  the  grid. 

106.  The  nickel-iron  storage  cell.  —  When  the  nickel-iron  cell 
is  fully  charged  it  has  a  positive  electrode  of  nickel  peroxide 
(NiOo),  a  negative  electrode  of  spongy  metallic  iron  (Fe),  and 
the  electrolyte  is  a  solution  of  caustic  potash  (KOH).  When 
the  cell  discharges,  the  nickel  peroxide  is  reduced  to  nickel  oxide 
and  the  spongy  metallic  iron  is  oxidized. 

The  nickel  peroxide  and  the  spongy  metallic  iron  (or  the  nickel 
and  iron  oxides  into  which  these  materials  are  converted  by 
discharge)  constitute  the  active  electrode  materials  of  the  nickel- 
iron  cell.  These  active  materials  are  held  in  grooves  or  pockets, 
in  plates  or  grids  of  metallic  nickel  and  steel. 

The  chemical  actions  which  take  place  in  the  charging  and 
discharging  of  the  nickel-iron  storage  cell  are  shown  in  the  fol- 
lowing schedule: 

DISCHARGING. 
Positive  grid      K   +  J(NiOj)  +  5(H2O)  =  £(NiO)  +  KOH 

L     Direction  of  current  through  the  cell. 
Negative  grid  OH  +  £Fe  =  |(FeO)  +  l(HjO) 

*  The  increase  and  decrease  of  voltage  during  charging  and  discharging  are  also 
due  in  part  to  the  resistance  of  the  cell  and  in  part  to  what  is  called  irreversible 
actions  at  the  electrodes. 


206  ELECTRIC   LIGHTING. 

CHARGING. 
Positive  grid    OH  +  i(NiO)  =  i(NiOi)  +  £(H,O) 

f    Direction  of  current  through  the  cell. 
Negative  grid    K  +  |(FeO)  +  |(H2O)  =  |Fe         +  KOH 

Effects  of  charge  and  discharge. — The  NiO2  contracts  and  the  Fe 
expands  during  discharge,  and  vice  versa]  but  there  is  no  general 
increase  or  decrease  of  concentration  of  the  electrolyte  due  to 
charging  and  discharging.  During  discharge,  however,  there 
is  an  increase  of  concentration  near  the  positive  grid  and  a  de- 
crease of  concentration  near  the  negative  grid  and  vice  versa. 

107.  Charging  and  discharging  curves.  Comparison  of  the 
lead  storage  cell  and  the  nickel-iron  storage  cell. — The  ordinates 
of  the  curve  in  Fig.  123  show  the  change  of  voltage  between  the 


Fig.  123. 

terminals  of  a  "3O-ampere"  lead  storage  cell  when  it  is  charged 
for  8  hours  and  discharged  for  8  hours,  the  current  being  30 
amperes  in  each  case.  The  ordinates  of  the  curve  in  Fig.  124 
show  the  change  of  voltage  between  the  terminals  of  a  "30- 
ampere"  nickel-iron  storage  cell  when  it  is  charged  for  5.5  hours 
and  discharged  for  5  hours,  the  current  being  30  amperes  in  each 
case. 


ELECTROLYSIS   AND    BATTERIES. 


207 


From  these  figures  it  is  evident  that  the  voltage  of  a  lead 
storage  cell  stands  at  a  more  nearly  constant  value  during  dis- 
charge than  the  voltage  of  a  nickel-iron  storage  cell.  The  average 
voltage  of  a  lead  cell  while  discharging  is  about  81  per  cent,  of 
the  average  voltage  while  being  discharged,  whereas  the  average 


volt 

r.?o 
.1.60 
•1.50 
140 


1,20 
t  • 
1.10 


hours 


discharge 


•>  4  S  6 

Fig.  124. 

voltage  of  a  nickel-iron  cell  while  discharging  is  about  72  per  cent, 
of  the  average  voltage  while  being  charged  The  energy  effi- 
ciency of  a  lead  storage  cell  when  charged  and  discharged  as 
represented  by  the  curves  in  Fig.  123,  is  about  80  per  cent.;  and 
the  energy  efficiency  of  a  nickel-iron  cell  when  charged  and  dis- 
charged, as  represented  by  the  curves  in  Fig.  124,  is  about  60 
per  cent. 

The  nickel-iron  storage  cell  seems  to  make  a  better  portable 
cell  than  the  lead  storage  cell  because  the  nickel-iron  cell  is 
lighter  than  the  lead  cell  and  because  the  nickel-iron  cell  may 
be  allowed  to  stand  for  a  long  time  partially  or  wholly  discharged. 
Also  the  nickel-iron  cell  is  perhaps  better  than  the  lead  storage 
cell  for  driving  electric  vehicles  because  the  nickel-iron  cell  does 
not  demand  careful  attention.  For  electric  vehicle  driving  a 
constant-voltage  supply  of  current  is  not  necessary  and  therefore 
the  great  change  of  voltage  of  the  nickel-iron  cell  is  not  especially 
objectionable  for  this  kind  of  service. 


208 


ELECTRIC    LIGHTING. 


The  lead  storage  battery  is  better  than  the  nickel-iron  storage 
battery  for  stationary  service  of  all  kinds  because  of  its  lower 
first  cost,  because  of  its  more  nearly  constant  voltage,  and  because 
of  its  higher  efficiency.  The  greater  constancy  of  voltage  is 
especially  important  when  current  is  to  be  supplied  to  incan- 
descent lamps;  the  voltage  even  of  a  lead  storage  battery  must 
be  regulated  when  it  is  used  for  this  purpose. 

108.  Portable  type  and  stationary  type  of  storage  cells.  Costs 
and  weights. — There  are  two  more  or  less  distinct  types  of  lead 
storage  cells,  namely,  the  portable  type  which  is  made  as  light 
as  possible  by  using  thin  grids  and  hard-rubber  containing  jars, 
and  the  stationary  type  which  has  very  heavy  grids  and  glass 
jars,  or,  in  the  case  of  very  large  cells,  lead-lined  wooden  tanks. 

The  portable  type  of  lead  storage  cell  has  about  10  watt-hours 
of  storage  capacity  (a  normal  discharge  rate  of  1.25  watts)  per 
pound  of  gross  weight.  The  stationary  type  of  lead  storage  cell 
has  about  4  watt-hours  of  storage  capacity  (a  normal  discharge 
rate  of  0.5  watt)  per  pound  of  gross  weight.  The  nickel-iron 
storage  cell  has  about  14  watt-hours  (2.8  watts  normal  discharge 
rate)  per  pound  of  gross  weight. 

Some  idea  of  the  cost  of  storage  cells  is  given  by  the  following 
schedules : 

LEAD  STORAGE  BATTERY,  HEAVY  STATIONARY  TYPE,   50  CELLS,  400  AMPERE- 
HOURS. 

To  deliver  5  kilowatts  for  8  hours.* 


Cost. 

Weight. 

Total. 

Per 
Kilowatt-hour 
of  capacity. 

Total. 

Per 
Kilowatt-hour 
of  capacity. 

In  glass  jars        . 

$1,400 
1,650 

$35.oo 
41.25 

10,300  Ibs. 
14,600 

258  Ibs. 
365 

In  lead-lined  wooden  tanks, 

Depreciation  6  or  7  per  cent,  per  year  when  properly  cared  for. 

*  Or  7  kilowatts  for  5  hours,  or  10  kilowatts  for  3  hours,  or  20  kilowatts  for  i 
hour.     See  page  211. 


ELECTROLYSIS    AND    BATTERIES. 


209 


LEAD  STORAGE  BATTERY,  LIGHT  PORTABLE  TYPE,  50  CELLS,  200  AMPERE-HOURS. 
To  deliver  2.5  kilowatts  for  8  hours.* 


* 

Cost. 

Weight. 

Total. 

Per 
Kilowatt-hour 
of  capacity. 

Total. 

Per 

Kilowatt-hour 
of  capacity. 

In  covered  rubber  jars  

$800 

540 

2,340  Ibs. 

117  Ibs. 

Depreciation  15  per  cent,  per  year  or  more. 

NICKEL-IRON  BATTERY,  60  CELLS,  225  AMPERE-HOURS. 
To  deliver  3.24  kilowatts  for  5  hours. 


Cost. 

Weight. 

Total. 

Per 
Kilowatt-hour 
of  Capacity. 

Total. 

Per 
Kilowatt-hour 
of  Capacity. 

In  covered  steel  tanks  

$960 

$59-25 

1,200  Ibs. 

71  Ibs. 

Depreciation  unknown. 

109.  Comparative  costs  of  electrical  energy  from  storage 
batteries  and  from  ordinary  primary  batteries. — (a)  A  storage 
battery  is  essentially  like  any  ordinary  battery  except  that  a 
storage  battery  can  be  regenerated  by  forcing  a  current  through 
it  backwards.  A  storage  battery  which  has  delivered  one  kilo- 
watt-hour of  electrical  energy  can  be  made  as  good  as  new  by 
the  expending  of  a  little  more  than  a  kilowatt-hour  in  forcing 
current  backwards  through  the  battery  at  a  cost  of  say  20  cents. 
Therefore,  the  output  of  a  storage  battery  may  cost  as  low  as  20 
cents  per  kilowatt-hour. 

(b)  A  Grenet  or  Fuller  cell  can  be  regenerated  after  use  by 
replacing  the  zinc  and  the  electrolyte.  Therefore  the  cost  of 
the  electrical  energy  delivered  by  a  Grenet  or  Fuller  cell  is  equal 
to  the  cost  of  the  materials  consumed  plus  a  few  cents  for  the 
labor  of  setting  up  the  cell.  The  voltaic  action  corresponding  to 
100  ampere-hours  represents  the  consumption  of  0.26  pound  of 
zinc  at  15  cents  per  pound,  0.40  pound  of  potassium  bichromate 

*  Or  3.5  kilowatts  for  5  hours,  or  5  kilowatts  for  3  hours,  or  10  kilowatts  for  I 
hour. 

15 


210  ELECTRIC   LIGHTING. 

at  15  cents  per  pound  and  0.6  pound  of  sulphuric  acid  at  2  cents 
per  pound  (the  zinc  is  reckoned  considerably  higher  in  price 
than  ingot  zinc  for  several  reasons,  one  of  which  is  the  cost  of 
mercury  for  amalgamating  the  zinc).  Therefore,  counting  five 
cents  for  the  labor  cost  we  have  a  total  cost  of  16.1  cents  for  100 
ampere-hours.  The  electromotive  force  of  the  bichromate  cell 
is  about  2  volts,  therefore  100  ampere-hours  represents  200  watt- 
hours,  and  200  watt-hours  at  16.1  cents  gives  a  rate  of  80  .cents 
per  kilowatt-hour.  But  the  total  consumption  of  materials  in 
a  Grenet  cell  is  at  least  five  times  the  consumption  corresponding 
to  the  voltaic  action  alone,  and  the  total  consumption  of  materials 
in  a  Fuller  cell  is  at  least  two  times  the  consumption  corresponding 
to  the  voltaic  action  alone.  Therefore  the  output  of  a  Grenet 
cell  costs  about  $4.00  per  kilowatt-hour  and  the  output  of  a 
Fuller  cell  costs  about  $1.60  per  kilowatt-hour. 

(c)  When  an  ordinary  dry  cell  is  discharged  the  entire  cell  is 
thrown  away,  and  therefore,  the  first  cost  of  the  cell  is  the  cost  of 
its  output  of  electrical  energy.  Thus  a  dry  cell  costing  25  cents 
has  about  50  ampere-hours  of  discharge  capacity  at  1.6  volts* 
which  is  equivalent  to  80  watt-hours,  and  25  cents  for  80  watt- 
hours  is  at  the  rate  of  $3.12  per  kilowatt-hour. 

Comparing  (a),  (b)  and  (c)  it  is  evident  that  a  storage  battery 
is  very  much  cheaper  than  an  ordinary  primary  battery  provided 
the  storage  battery  can  be  charged  without  excessive  loss  of 
energy  in  a  rheostat  and  without  carrying  the  battery  to  a 
charging  station.  The  following  example  shows  the  excessive 
cost  of  a  storage  battery  where  these  two  conditions  are  not 
realized.  A  three-cell  storage  battery  having  a  capacity  of  50 
ampere-hours  at  6  volts  is  delivered  to  the  proper  place  for 
charging  at  a  cost  of  50  cents  counting  return  delivery  and  the 
battery  is  charged  from  no- volt  direct-current  mains  so  that 
5,500  watt-hours  f  of  energy  is  consumed  in  charging  the  battery. 

*  No  allowance  is  here  made  for  the  fact  that  the  terminal  voltage  of  the  cell 
may  be  considerably  less  than  its  open-circuit  voltage. 

t  The  battery  would  be  connected  to  the  supply  mains  in  series  with  a  rheostat 
and  about  94  per  cent,  of  the  energy  taken  from  the  mains  would  be  lost  in  this 


ELECTROLYSIS   AND    BATTERIES.  211 

At  15  cents  per  kilowatt-hour  this  energy  amounts  to  82  cents, 
and  the  total  cost  of  $1.32  for  charging  the  battery  is  the  cost 
of  the  300  watt-hours*  of  battery  output,  which  is  at  the  rate  of 
$4.40  per  kilowatt-hour. 

no.  The  management  and  care  of  a  lead  storage  battery.* — 

The  lead  storage  battery  deteriorates  rapidly  in  service  when  it  is 
not  properly  cared  for,  and,  the  first  cost  of  the  storage  battery 
being'high,  it  is  important  that  it  should  have  proper  care.  The 
deterioration  shows  itself  by  a  decrease  of  ampere-hour  capacity, 
by  a  continued  disintegration  of  the  active  materials  of  the 
electrodes,  by  a  slow  corrosion  of  the  massive  lead  grids  and  by 
warping  and  buckling  of  the  grids. 

Setting  up  a  storage  battery. — Detailed  directions  for  setting  up 
a  storage  battery  are  always  supplied  by  the  manufacturer.  A 
person  who  has  not  had  experience  in  handling  acids  must 
exercise  great  care.  The  concentrated  acid  should  be  poured 
into  the  water  in  a  thin  stream  and  the  water  should  be  stirred 
with  a  wooden  paddle,  great  care  being  taken  to  avoid  splashing. 
The  acid  should  be  mixed  in  an  earthenware  jar  or  in  a  clean 
wooden  tub.  Metal  must  not  be  used. 

The  electrolyte. — The  electrolyte  is  dilute  sulphuric  acid  having 
a  density  of  about  1.21  at  70°  F.  when  the  battery  is  charged. 
This  acid  must  be  quite  pure  (free  from  iron,  hydrochloric  acid 
or  nitric  acid),  and  pure  water,  preferably  distilled  water,  must 
be  used  for  mixing  the  electrolyte. 

When  the  surface  of  the  electrolyte  falls  because  of  evaporation, 
pure  water  must  be  added  so  as  to  keep  the  tops  of  the  grids 
covered  to  a  depth  of  about  one-half  inch. 

Discharging. — The  normal  discharge  current  of  a  lead  storage 

rheostat.  To  avoid  this  loss  of  energy  many  storage  cells  must  be  connected  in 
series  for  charging  from  no- volt  mams. 

*See  Chapters  XXII  and  XXIII  of  Lyndon's  Storage  Battery  Engineering, 
McGraw-Hill  Book  Company,  1911. 

Manufacturers  of  storage  batteries  publish  circulars  giving  instructions  for 
setting  up  and  operating,  and  the  manufacturers  are  usually  glad  to  send  these 
circulars  to  any  one  who  is  interested  in  storage  battery  work. 


212  ELECTRIC   LIGHTING. 

cell  (on  the  basis  of  an  eight-hour  discharge)  is  about  5  amperes 
per  square  foot  of  positive  grid  area,  both  sides  of  each  positive 
grid  being  counted. 

A  current  exceeding  4  or  5  times  the  normal  discharge  current 
should  never  be  taken  from  a  storage  cell;  if  a  greater  current 
must  be  taken  from  a  cell  it  should  be  for  a  few  minutes  only 
and  the  battery  should  be  at  full  charge. 

A  lead  storage  battery  should  never  be  discharged  so* as  to 
cause  the  voltage  to  drop  below  1.75  volts  per  cell,  while  the 
normal  discharge  current  is  flowing. 

A  lead  storage  cell  should  never  be  allowed  to  stand  discharged. 

Charging. — Usually  a  lead  storage  battery  is  charged  by  a  cur- 
rent equal  to  the  normal  discharge  current,  the  time  required 
for  charging  being  eight  or  eight  and  one-half  hours. 

The  charging  current  may  be  high,  however,  when  the  battery 
is  nearly  discharged,  and  it  should  be  low  when  the  battery 
approaches  full  charge,  especially  after  evolution  of  gas  begins. 
A  good  rule  for  rapid  charging  is  to  deliver  35  per  cent,  of  the 
total  ampere-hours  during  the  first  hour,  52  per  cent,  during  the 
next  two  hours,  and  14  per  cent,  during  the  fourth  hour.  Thus  a 
loo-ampere-hour  cell  may  be  completely  charged  in  four  hours  by 
using  a  charging  current  of  35  amperes  during  the  first  hour,  26 
amperes  during  the  second  and  third  hours,  and  14  amperes 
during  the  fourth  hour. 

Overcharging. — A  battery  should  be  overcharged  once  a  week, 
or  once  every  two  weeks  if  it  is  not  used  daily.  This  overcharge 
is  a  prolongation  of  the  regular  charge  (at  the  normal  eight-hour 
rate)  until  the  voltage  across  each  cell  reaches  a  maximum,  that 
is,  until  five  successive  voltmeter  readings,  15  minutes  apart, 
show  no  further  increase  of  voltage,  or  until  gas  is  developed  in 
all  the  cells  freely. 

Voltmeter  test. — The  voltage  of  each  cell  should  be  taken  just 
before  the  end  of  the  weekly  overcharge  with  current  flowing  at  the 
normal  eight-hour  rate.  The  normal  voltage  under  these  con- 
ditions is  about  2.56  volts  per  cell.  The  voltage  normally  reached 


ELECTROLYSIS   AND    BATTERIES.  213 

during  the  regular  charging  is  about  2.45  volts  per  cell.  An 
abnormally  low  voltage  shows  that  a  cell  has  been  discharged 
by  internal  short  circuit. 

Inspection. — Just  before  the  weekly  overcharge,  every  cell 
should  be  inspected  carefully,  especial  attention  being  given  to 
those  cells  which  have  shown  abnormally  low  voltage  on  previous 
tests.  The  object  of  the  inspection  is  to  see  that  no  internal 
short  circuits  exist.  Short  circuits  are  to  be  removed  by  means  of 
a  thin  strip  of  hard  wood  pushed  down  between  the  grids.  Evi- 
dences of  sulphatation  should  also  be  noted  as  explained  under 
the  heading  sulphatation. 

Treatment  of  cells  which  show  abnormally  low  voltage. — If  the 
voltage  of  a  cell  does  not  rise  to  the  normal  value  during  an 
overcharge,  it  must  be  cut  out  of  circuit  when  the  battery  is  dis- 
charged and  cut  in  again  just  before  beginning  the  next  charging. 
If  this  does  not  bring  it  up  to  normal  voltage  the  process  must 
be  repeated. 

Sediment. — The  accumulation  of  sediment  in  the  bottom  of  the 
jars  must  be  watched  and  the  sediment  must  be  removed  before 
it  reaches  the  bottom  of  the  grids.  In  the  case  of  small  cells 
the  grids  may  be  lifted  out  after  the  battery  has  been  fully 
charged,  the  electrolyte  drawn  off,  and  the  sediment  washed 
out  of  the  jars.  It  is  important  to  get  the  elements  back  and 
covered  with  electrolyte  again  as  quickly  as  possible.  Fresh 
electrolyte  must  be  added  to  make  up  for  the  electrolyte  lost 
with  the  sediment. 

Sulphatation. — Sulphatation  of  the  grids  of  a  lead  storage  cell 
consists*  of  the  conversion  of  portions  of  the  active  material 
wholly  into  lead  sulphate.  This  pure  sulphate  is  a  very  poor 
conductor  and,  once  it  is  formed,  it  is  difficult  to  make  it  act  as 
anode  or  as  cathode  and  thus  reconvert  it  to  lead  peroxide  or  to 
spongy  lead  respectively.  A  layer  of  pure  lead  sulphate  some- 
times forms  between  the  active  material  and  the  metallic  lead 

*  It  is  claimed  by  some  authorities  that  sulphatation  consists  in  the  formation 
of  hydrated  lead  sulphate. 


214  ELECTRIC    LIGHTING. 

of  the  grid,  and  sometimes  the  external  surface  of  the  active 
material  becomes  covered  with  a  crust  of  pure  sulphate.  Pure 
lead  sulphate  is  white  and  whenever  white  spots  appear  on  the 
grids  of  a  lead  storage  cell,  the  cell  should  be  subjected  to  a  very 
long-continued  over-charge  in  the  attempt  to  reduce  the  pure 
lead  sulphate  into  active  material. 

A  very  good  method*  for  treating  sulphated  cells  is  as  follows: 

1.  Remove  the  acid  electrolyte  and  rinse  with  pure  water. 

2.  Fill  the  cells  with  a  solution  of  pure  sodium  sulphate  using 
200  grams  of  the  crystallized  salt  per  liter  of  water. 

3.  Charge  the  battery  in  the  usual  way  at  the  8-hour  rate  for 
50  hours  or  more. 

4.  Remove  the  sodium  sulphate  solution  and  rinse  with  pure 
water. 

5.  Replace  the  acid  electrolyte,  using  a  little  fresh  acid  to 
bring  it  up  to  correct  strength. 

6.  Charge  the  battery 

One  change  of  water  is  sufficient  for  each  rinsing.  The  cost 
of  the  entire  treatment  counting  labor,  materials  and  energy  is 
about  21  cents  per  cell  for  cells  rated  at  6o-ampere-hours. 

Variation  of  capacity  with  discharge  rate. — When  a  storage  cell 
is  discharged  slowly,  the  discharge  can  be  carried  further  than 
when  the  cell  is  discharged  rapidly,  that  is  to  say,  the  ampere-hour 
capacity  is  greater  with  a  small  ampere  discharge  than  with  a 
large  ampere  discharge.  The  relation  between  ampere-hours  of 
capacity  and  amperes  of  discharge  rate  for  the  stationary  bat- 
teries of  the  Electric  Storage  Battery  Company  is  as  follows: 
A  cell  that  can  deliver  12.5  amperes  for  eight  hours  can  deliver 
17.5  amperes  for  five  hours,  25  amperes  for  three  hours  or  50 
amperes  for  one  hour. 

in.  The  use  of  storage  batteries.f — Storage  batteries  are  ex- 
tensively used  in  the  place  of  ordinary  primary  batteries  in 

*See  a  paper  by  C.  W.  Bennett  and  D.  S.  Cale;  read  before  the  Boston  Gen- 
eral Meeting  of  the  American  Electrochemical  Society,  April  18,  1912. 

t  Fundamentally,  of  course,  a  storage  battery  is  used  to  store  electrical  energy 
at  a  given  time  and  place  in  order  that  the  energy  may  be  used  when  and  where 
it  is  needed. 


ELECTROLYSIS   AND    BATTERIES. 


215 


telephone  and  telegraph  work  and  in  railway  signalling.*  Stor- 
age batteries  are  also  used  for  driving  electric  vehicles  and  for 
railway  car  lighting,  and  very  large  storage  batteries  are  used  in 
central  stations  for  one  or  more  of  the  following  purposes: 

(a)  For  supplying  the  station  output  during  the  hours  of  small 
demand.  In  this  case  the  battery  is  charged  while  the  station 
is  in  operation,  and  discharged  during  the  remainder  of  the  day, 
thus  obviating  the  expense  of  operating  the  station  continuously. 


280 


240 


160 


6 
AM 


charge^ 


/discharge 


^ 


10  12  2 

Fig.  125. 


6 
PM 


(b)  For  equalizing  a  fluctuating  station  load.  In  this  case  pro- 
vision is  made  for  the  battery  to  charge  while  the  station  load 
is  below  the  average  and  to  discharge  while  the  station  load 
is  above  the  average.  This  is  an  important  use  of  large  storage 
battery  installations,  and  the  cost  of  installing  and  maintaining 
the  battery  is  set  over  against  the  saving  in  the  first  cost  of  the 
station  and  the  saving  in  the  cost  of  operating  the  station. 

*  In  many  cases  a  small  motor-generator  is  used  to  take  current  from  no- volt 
mains  (direct-current  or  alternating-current)  and  deliver  direct  current  at  low  voltage 
for  charging.  In  some  cases  direct  current  for  charging  is  derived  from  alternating- 
current  supply  mains  by  using  the  mercury-vapor  rectifier. 


216 


ELECTRIC    LIGHTING. 


(c)  As  a  reserve. — The  primary  object  of  a  storage  battery 
may  be  to  supply  the  output  of  a  station  during  certain  hours 
of  the  day  or  to  equalize  a  fluctuating  load  on  a  station.  In  both 
cases  the  battery  will  be  valuable  also  as  a  reserve  to  supply  the 
station  load  in  case  of  a  break-down. 

Figure  125  illustrates  the  use  of  a  storage  battery  for  supplying 
the  total  station  output  during  the  hours  of  small  demand.  The 


10 


12        3.        6         9       12        3         6        9        12 


curve  represents  the  operation  of  a  small  direct-current  plant  at 
Milan,  Michigan,  in  1902.  The  engine  and  generators  were 
operated  from  5:30  P.  M.  to  10:30  P.  M.  From  5:30  to  about 
6:20  P.  M.  the  generators  supply  the  station  load  (which  is  small) 
and  charge  the  battery.  Between  6:20  P.  M.  and  8:40  P.  M. 
the  generators  supply  the  station  load,  only,  and  the  battery  is 
disconnected.  Then  from  8:40  P.  M.  until  10:30  P.  M.  the 
generators  supply  the  station  load  (which  is  small)  and  charge 
the  battery.  The  engine  is  shut  down  at  10:30  P.  M.  and  the 
battery  carries  the  entire  station  load  until  5  :3O  the  next  evening. 
The  use  of  a  storage  battery  for  equalizing  the  load  on  a 


ELECTROLYSIS   AND   BATTERIES. 


217 


generator  is  shown  in  Fig.  126.  This  curve  shows  the  operation 
of  the  central  station  of  the  Hartford  Electric  Light  Company  on 
December  n,  1905.  The  battery  was  charged  from  about  10:30 
P.  M.  to  6  A.  M.,  and  discharged  from  about  4  P.  M.  to  10:30 
P.  M.,  during  the  peak  of  the  station  load. 

The  use  of  a  storage  battery  for  equalizing  the  rapidly  fluctuat- 
ing load  of  an  electric  railway  station  is  shown  in  Fig.  127.  The 
dotted  curve  in  this  figure  shows  the  actual  generator  load  and 


CONNECTICUT  Railway  AND  LUSHTING*  Co 

New  Bn 
I  I  I  I  I 


Fig.  127. 

the  full-line  curve  shows  the  rapidly  fluctuating  station  load  be- 
tween 12  :o6  P.  M.  and  12:15  P.  M.  Readings  were  taken  every 
five  seconds. 

The  use  of  a  storage  battery  as  represented  in  Figs.  125,  126 
and  127  depends  upon  the  employment  of  controlling  devices 
as  described  in  the  following  articles. 

112.  The  use  of  a  storage  battery  for  supplying  the  output  of 
a  station  during  the  hours  of  small  demand. — When  a  storage 
battery  is  used  for  this  purpose  it  is  nearly  always  desired  to 


21 8  ELECTRIC   LIGHTING. 

deliver  current  at  constant  voltage,  and  some  device  for  con- 
trolling the  voltage  of  the  battery  is  necessary  as  explained  below. 
A  sufficient  number  of  storage  cells  is  used  to  give  the  required 
voltage  when  the  battery  is  discharged  and  has  1.8  volts  per  cell, 
and  the  controlling  device  is  arranged  to  take  up  the  excess 
voltage  when  the  battery  voltage  is  higher  than  the  desired  value. 
Control  of  voltage  by  rheostat. — The  current,  /,  delivered  by 
the  battery  flows  through  a  resistance,  R,  Fig.  128,  and  this 
resistance  is  adjusted  so  that  the  excess  of  battery  voltage  may 
be  used  up  as  the  voltage  drop  RI  in  this  resistance.  When  the 
station  output  is  constant  this  method  of  control  is  fairly  satis- 
factory, for,  in  this  case,  the  resistance  has  to  be  adjusted  only 
occasionally  as  the  battery  voltage  falls  off.  When  the  station 
output  fluctuates,  however,  the  rheostat,  R,  Fig.  128,  requires 
constant  attention  because  the  voltage  drop  RI  in  the  rheostat 
changes  when  the  station  output  changes. 

Control    of  voltage   by  counter-electromotive-force  cells. — When 
current  flows  through  a  low-resistance  electrolytic  cell  consisting 

of  plain  lead  plates  in  dilute  sul- 
phuric acid,  the  voltage  drop 
through  the  cell  varies  from  about 
2.3  to  2.5  volts  according  to  the 
value  of  the  current.  The  excess 
voltage  of  a  discharging  storage 
battery  may  be  taken  up  by  caus- 
ing the  current  to  flow  through  a 
number  of  such  cells  connected  in 
series,  the  number  being  reduced 

as  the  battery  voltage  decreases. 
to  lamps 

The    advantage    of   this  arrange- 


Fig  12g  ment  is  that  the  voltage  which  is 

lost  in  these  controlling  cells  does 

not  vary  greatly  with  the  current.  This  method  of  voltage  con- 
trol is  seldom  used  in  practice.  It  has  no  advantage  over  the 
rheostat  method  when  the  load  is  constant,  and  the  end-cell 
method  is  usually  preferred  when  the  load  is  variable. 


ELECTROLYSIS   AND    BATTERIES 


219 


Control  of  voltage  by  end-cells. — This  method  of  control  will  be 
explained  by  giving  an  actual  example  of  a  battery  delivering 
current  at  no  volts. ,  The  lowest  permissible  voltage  at  the  end 
of  the  discharge  is  usually  taken  to  be  1.8  volts  per  cell.  There- 
fore the  number  of  cells  required  to  give  a  minimum  of  no  volts 
is  no  -f-  1.8,  which  is  equal  to  61.  The  highest  voltage  is  about 
2.15  volts  per  cell  at  the  very  beginning  of  the  discharge  (see 
Fig.  123),  and  51  cells  are  therefore  required  at  the  very  beginning 
of  the  discharge  to  give  no  volts.  Therefore,  the  entire  battery 
being  fully  charged,  51  cells  are  used  at  the  beginning  of  the  dis- 
charge, and  as  the  voltage  of  the  battery  falls  off  the  number  of 
cells  is  increased,  by  connecting-in  additional  cells  at  one  end  of 
the  set,  until,  when  the  battery  reaches  the  limit  of  discharge, 
all  of  the  6 1  cells  are  in  service.  Under  these  conditions  it  is 
evident  that  the  end-cells,  which  are  in  service  only  a  portion  of 
the  time  during  the  delivery  of  current  by  the  battery,  are  not 
completely  discharged  Therefore,  when  the  battery  is  re- 
charged, the  end-cells  are  placed  in  circuit  at  the  start  and  cut 
out  one  by  one  as  they  become 
fully  charged,  as  indicated,  for 
example,  by  the  copious  evolu- 
tion of  gas. 

An  important  detail  in  the  car- 
rying out  of  the  end-cell  method 
of  voltage  control  is  the  design 
of  the  switch  for  connecting  and 
disconnecting  the  end-cells  with- 
out interrupting  the  delivery  of 
current,  and  without  momen- 
tarily short-circuiting  the  indi- 
vidual cells.  The  essential  fea- 
tures of  this  end-cell  switch*  are 

shown   in    Fig.    129.     The    terminals     of     the     end-cells     are 
brought  out  to  a  series  of   contact    blocks,     cccc,     which    are 

*  Various  types  of  end-cell  switches  are  described  on  pages  285-324  of  Lyndon's 
Storage  Battery  Engineering. 


Fig.  129. 


220 


ELECTRIC    LIGHTING. 


rather  widely  separated  from  each  othep.  The  movable  con- 
tact arm  of  the  connecting  and  disconnecting  device  has  two  fin- 
gers, a  and  b,  which  are  far  enough  apart  to  bridge  across  be- 
tween two  of  the  blocks  cc  as  shown  in  the  figure.  When  the 
contact  arm  is  moved  it  stands  for  a  moment  in  the  position 
shown  in  the  figure  and  short-circuits  one  of  the  cells  of  the  bat- 
tery, but  this  short-circuit  takes  place  through  the  resistance  R 
so  that  no  damage  is  done.  The  contact  arm  is  arranged  to  move 
quickly  past  the  position  shown  in  the  figure  and  stand  with  both 
fingers  a  and  b  in  contact  with  one  of  the  blocks  c. 

113.  The  booster. — Consider,  for  exam  pie,  the  use  of  a  storage 
battery  for  supplying  the  output  of  a  station  during  the  hours 
of  small  demand,  the  voltage  of  the  station  being,  say,  no  volts. 
A  battery  of  61  cells  would  be  required  as  explained  above,  and  to 
charge  such  a  battery  a  voltage  of  about  150  volts  would  be 


Main 


Main 


Fig.  130. 

required  towards  the  end  of  the  charge  (2.45  volts  per  cell). 
Now  the  battery  is  usually  charged  from  the  main  generator 
of  the  station  while  the  generator  is  supplying  regular  station  out- 
put at  no  volts,  and  therefore  the  generator  voltage  is  not 
sufficient  to  charge  the  battery.  In  practice  a  small  auxiliary 
generator  B,  Fig.  130,  is  connected  in  series  with  the  storage 


ELECTROLYSIS   AND   BATTERIES. 


221 


battery  and  this  auxiliary  generator  helps  to  force  the  charging 
current  through  the  battery.  The  auxiliary  generator  B  is 
called  a  booster. 

114.  Automatic  boosters.* — When  the  station  load  changes 
slowly,  as  is  usually  the  case  in  an  electric  lighting  station,  there 
is  ample  time  for  an  attendant  to  connect  up  a  booster  and  charge 
a  storage  battery  when  the  station  load  is  small,  and  to  disconnect 
the  booster  and  make  the  necessary  arrangements  for  discharging 
the  battery  when  the  peak  of  the  load  comes  on.  When,  how- 
ever, the  station  load  fluctuates  rapidly  and  irregularly  as  is 
usually  the  case  in  an  electric  railway  power  station,  hand  control 
of  the  storage  battery  is  impossible.  In  such  cases  an  automatic 
booster  must  be  used. 

The  differential  booster. — Fig.  131  shows  an  arrangement, 
due  to  Mailloux,  in  which  a  booster,  B,  is  actuated  by  variations 


Fig.  131. 

of  line  current.  The  booster  has  two  opposing  field  windings, 
5  and  S'.  When  the  demand  for  current  is  at  its  average  value 
the  windings,  5  and  5',  balance  each  other,  the  small  generator, 
B,  develops  no  electromotive  force,  and  the  battery  neither 
charges  nor  discharges.  When  the  line  current  is  excessive  the 

*  A  very  full  discussion  of  boosters  and  booster  systems  is  given  on  pages  325-470 
of  Lyndon's  Storage  Battery  Engineering. 


222 


ELECTRIC   LIGHTING. 


winding,  S,  predominates,  and  the  voltage  of  B  helps  the  bat- 
tery to  discharge;  when,  however,  the  line  current  is  small  the 
winding,  S',  predominates  and  the  reversed  voltage  of  B  helps 
the  line  voltage  to  charge  the  battery. 

Booster  with  automatic  carbon  rheostat  control. — Fig.  132 
shows  a  carbon  rheostat,  RRf,  connected  across  the  terminals  of 
the  storage  battery ;  and  the  field  winding,  F,  of  the  booster,  B, 
is  connected  from  the  middle  of  the  rheostat  to  the  middle  of  the 
battery.  The  solenoid  S  pulls  on  an  iron  plunger  which  is 
attached  to  one  end  of  the  lever  II  and  two  lugs  on  this  lever 
push  on  two  piles  of  carbon  plates  R  and  Rf  which  constitute 
the  rheostat.  A  large  line  current  gives  a  strong  pull  of  the 
solenoid  which  compresses  the  pile  R  of  carbon  plates  and  greatly 


Line 


Line 


Fig.  132. 

reduces  its  resistance.  A  small  line  current  reduces  the  pull  of 
the  solenoid  and  the  pull  of  the  spring  compresses  the  pile  of  Rf 
of  carbon  plates  thus  greatly  reducing  its  resistance.  The  current 
in  the  field  winding  F  of  the  booster  is  zero  when  the  resistances 
of  R  and  R'  are  equal,  and  the  current  through  the  field  winding 


ELECTROLYSIS   AND    BATTERIES.  223 

is  in  one  direction  when  R  is  greater  than  Rf  and  in  the  opposite 
direction  when  R  is  less  than  R'.  In  this  manner  the  field  of 
the  booster  is  so  excited  as  to  cause  the  booster  to  help  the 
storage  battery  discharge  when  the  station  output  is  large  and 
to  help  the  station  voltage  to  charge  the  battery  when  the 
station  output  is  small. 

The  ordinates  of  the  extremely  irregular  curve  in  Fig.  127 
represent  the  fluctuating  demand  for  current  on  a  railway  power 
station  during  a  period  of  ten  minutes.  Without  a  storage 
battery  the  generators  would  have  to  meet  this  extremely  irregular 
demand,  varying  from  a  minimum  of  about  180  amperes  to  a 
maximum  of  about  850  amperes.  The  ordinates  of  the  slightly 
undulating  dotted  curve  show  the  values  of  generator  output 
when  an  adequate  storage  battery  is  installed  and  controlled  by 
a  booster  as  shown  in  Fig.  132  with  the  field  excitation  of  the 
booster  under  the  control  of  a  carbon  rheostat.  When  the  total 
load  curve  is  above  the  dotted  curve  (generator  output)  the 
battery  discharges,  and  when  the  total  load  curve  is  below  the 
dotted  curve  the  battery  charges. 

The  general  average  of  the  generator  load  must  be  slightly 
greater  than  the  general  average  of  the  station  output  because 
some  energy  is  lost  in  the  battery,  but  the  average  generator 
load  during  a  short  period  may  be  greater  or  much  less  than  the 
average  station  output  during  that  period.  Thus  the  average 
station  output  during  the  ten  minute  period,  which  is  shown  in 
Fig.  127,  was  evidently  greater  than  the  average  generator 
load  during  that  period  so  that  the  battery  was  on  the  whole 
discharging.* 

115.  The  floating  battery. — The  simplest  arrangement  for 
causing  a  storage  battery  to  operate  automatically  and  tend  to 
equalize  a  station  load,  is  that  which  is  frequently  employed  in 
connection  with  long  feeders  over  which  a  considerable  drop  of 
voltage  takes  place  when  a  large  current  is  delivered.  This 

*  A  good  example  of  a  large  storage  battery  installation  is  described  by  Franklin 
E.  Moore  in  the  Street  Railway  Journal  for  September  21,  1911. 


224 


ELECTRIC   LIGHTING. 


arrangement  is  shown  in  Fig.  133,  in  which     G    is  the  main 
generator  and   B  is  the  storage  battery.     Any  great  demand  for 

Long  feeder  _•_-•.  , 


Long  feeder 


a 

(°X°3tl 


Fig.  133. 

current  causes  the  voltage,  E,  to  decrease,  so  that  the  battery 
can  discharge,  and  when  the  demand  for  current  is  small  the 
voltage,  .E,  rises  and  the  battery  is  charged.  A  battery  con- 
nected as  shown  in  Fig.  133  is  called  a  floating  battery.  Such  a 
floating  battery  cannot  completely  equalize  the  demand  on  the 
station,  inasmuch  as  the  rise  and  fall  of  the  voltage,  E,  depends 
upon  some  decrease  and  increase  of  the  current  flowing  through 
the  long  feeders. 

116.  The  negative  booster. — An  arrangement  which  produces 
an  effect  which  is  exactly  equivalent  to  Fig.  133  is  shown  in  Fig. 
A  generator    G   supplies  current  at  constant  voltage  and 


Tramps 


Fig.  134. 


an  elevator  motor  takes  current  from  the  constant  voltage  mains 
through  a  series  motor   SM.    This  series  motor  is  belted  to  the 


ELECTROLYSIS   AND    BATTERIES.  225 

main  generator  G  so  as  to  run  at  constant  speed,  and  so  that 
the  power  generated  by  SM  may  be  belted  back  to  the  main 
generator.  When  the  elevator  motor  takes  large  current  the  field 
of  the  series  motor  is  strongly  excited  and  its  counter  electro- 
motive force  is  large  so  that  the  voltage  E2  is  much  less  than  EI. 
Under  these  conditions  the  storage  battery  discharges.  When 
the  elevator  motor  takes  small  current  the  field  magnet  of  the 
series  motor  is  only  weakly  excited  and  its  counter  electromotive 
force  is  small  so  that  E%  is  nearly  as  large  as  EI  and  the  storage 
battery  charges. 

The  series  motor  SM  in  Fig.  134  is  called  a  negative  booster, 
and  the  loss  of  voltage  in  the  series  motor  due  to  its  counter 
electromotive  force  is  exactly  analogous  to  the  drop  of  voltage 
in  the  long  feeders  in  Fig.  133.  That  is  to  say  the  battery  in 
Fig.  134  acts  exactly  like  the  floating  battery  in  Fig.  133. 


16 


CHAPTER  IX. 

MISCELLANEOUS  APPLICATIONS. 

117.  The  Morse  telegraph.* — An  insulated  wire  leads  from 
one  station  to  another  and  back  again  (the  earth  is  generally 
used  instead  of  a  return  wire) .  An  electric  current  from  a  battery 
is  sent  intermittently  through  this  circuit  by  operating  at  one 
station  a  key  which  makes  and  breaks  the  circuit.  This  current 
excites  an  electromagnet  at  the  other  station,  and  the  armature 
of  this  electromagnet  makes  a  record  on  a  moving  strip  of  paper 
or  produces  sound  signals  which  are  interpreted  by  the  operator 
at  the  other  station. 

Relays  and  sounders. — A  fairly  strong  electric  current  is  re- 
quired to  operate  the  instrument  which  produces  the  signals  at 
the  receiving  station,  and  it  is  not  desirable  to  send  so  strong  a 
current  over  a  long  line  because  of  the  great  number  of  voltaic 
cells  that  would  be  required.  This  difficulty  is  obviated  by  the 
use  of  a  relay.  A  small  current  flows  over  the  line  and  through 
many  turns  of  fine  wire  wound  upon  an  electromagnet  (of  the 
relay)  at  the  receiving  station.  This  magnet  actuates  a  very 
light  lever,  and  this  lever  is  arranged  to  open  and  close  what  is 
called  a  local  circuit  as  it  moves  back  and  forth  between  stops. 
The  local  circuit  which  is  opened  and  closed  by  the  light  lever  of 
the  relay  contains  a  battery  which  supplies  a  moderately  large 
current  for  the  operation  of  the  instrument  which  produces  the 
sound  signals.  This  instrument  is  called  a  sounder.  It  consists 

*  A  good  treatise  on  telegraphy  is  American  Telegraphy  by  William  Maver,  Jr., 
New  York,  1892. 

It  is  not  practicable  to  operate  a  very  long  telegraph  line  as  one  circuit  for  reasons 
which  are  explained  in  the  article  on  submarine  telegraphy.  Long  circuits  are, 
therefore,  broken  up  into  sections.  In  the  early  days  messages  were  repeated 
from  one  section  to  another  by  hand,  but  an  automatic  device  called  a  repeater  is 
now  used. 

226 


MISCELLANEOUS   APPLICATIONS. 


227 


of  an  electromagnet  which  is  wound  with  moderately  coarse  wire 
and  which  actuates  a  massive  lever,  and  the  lever  produces  sharp 
clicks  as  it  moves  back  and  forth  between  stops. 

Way  stations. — An  ordinary  telegraph  may  include  relays 
placed  at  points  along  the  line,  and  a  make  and  break  key  may  be 
operated  at  any  point  along  the  line  if  all  the  other  keys  are 


local   battery 

Fig.  135. 

closed.  When  any  key  is  thus  operated  all  of  the  instruments 
on  the  line  respond  simultaneously.  The  simple  railway  tele- 
graph is  usually  arranged  in  this  manner.  It  is  not  unusual 
to  have  a  single  circuit  one  hundred  and  fifty  miles  or  more  in 
length  containing  fifteen  or  twenty  way  stations. 

The  arrangement  of  relay  and  sounder  is  shown  in  Fig.  135,  aa 
being  the  wires  which  connect  the  fine-wire  winding  on  the  relay  in 

home  station  way  station  distant  station 

key  keif 


INT 

_J relay 


ground 


relay 


Fig.  136. 


ground 


circuit  with  the  telegraph  line.  Figure  136  shows  a  simple 
telegraph  circuit  with  two  end  stations  and  one  way  station. 
The  local  circuits  and  sounders  (one  at  each  station)  are  omitted 
from  this  diagram  for  the  sake  of  clearness.  Of  course  all  of 


228 


ELECTRIC    LIGHTING. 


the  keys  are  normally  closed,  and  when  a  telegram  is  to  be  sent 
from  any  station  the  key  at  that  station  is  manipulated  so  as  to 
make  and  break  the  circuit  of  the  line. 

118.  Duplex  telegraphy. — The  sending  of  two  messages   (in 
opposite  directions)  over  one  line  wire  simultaneously  is  called 


000000(5000 


battery 


home  relay 

d(~  artificial  line) 

"UTblTo  o  o  o  o!T5 


Fig.  137. 

duplex  telegraphy.  There  are  two  systems  of  duplex  telegraphy, 
namely  the  bridge  duplex,  and  the  differential  duplex.  Way  sta- 
tions cannot  be  used  in  the  duplex  system. 

Figure  137  shows  the  principle  of  the  bridge  duplex.  The  four 
resistances  a,  b,  c,  and  d  constitute  a  Wheatstone  bridge  ar- 
rangement, and  no  portion  of  the  battery  Current  flows  through 
the  home  relay  when  the  home  key  ic  closed.  The  resistance  c 
represents  the  line  and  the  apparatus  at  the  distant  station  (which 
is  interpolated  at  p).  The  actual  arrangement  of  the  bridge 
home  station  ...  distant  statio* 


line 


key 


Fig.  138.     Bridge  duplex. 

duplex  is  shown  in  Fig.  138.  In  Fig.  138  the  distant  relay  re- 
sponds to  the  home  key  and  the  home  relay  responds  to  the  dis- 
tant key.  The  local  circuits  and  sounders  are  omitted  for  the 
sake  of  clearness. 


MISCELLANEOUS    APPLICATIONS. 


229 


The  differential  duplex  makes  use  of  the  differentially  wound 
relay  or  the  differential  relay,  and  the  principle  of  the  differential 
duplex  is  shown  in  Fig-  139.  The  battery  current  divides  equally 

c(=ttne) 


«! 

^ 

c.         b 
=-  bntteri 

^ 

,        00000000000 

home 
differential 
relay 

d(=  artificial  line) 

>* 

1 

00000000000 

Fig.  139. 

between  the  two  similar  branches  c  and  J,  and  the  two  equal 
parts  of  the  battery  current  circulate  in  opposite  directions  in  the 
two  windings  a  and  b  of  the  differential  relay  so  that  the  iron 
core  of  the  differential  relay  is  not  magnetized  when  the  key  is 
closed  in  Fig.  139.  The  resistance  c  represents  the  line  and  the 
apparatus  at  the  distant  station  (which  is  interpolated  at  p). 
The  actual  arrangement  of  the  differential  duplex  is  shown  in  Fig. 
140.  In  Fig.  140  the  distant  relay  responds  to  home  key  and 
the  home  relay  responds  to  the  distant  key.  The  local  circuits 
and  sounders  are  omitted  for  the  sake  of  clearness. 


home  station 

a 
key 

bf: 


line 


distant   station 
key 


-  ;  differential                                       differential  ^ 
^       relay                                                   relay      ;r; 

^        d 

?—                                                        **5S 

*    :: 

ry 

ound 

.11—.      ed 

ooooootftTtitP  *—"  ' 

fc 

fjrounc 

S-==S=5= 

Fig.  140.     Differential  duplex. 

The  bridge  duplex  prevails  in  Europe  and  especially  in  England, 
and  the  differential  duplex  is  almost  universal  in  the  United 
States.  The  bridge  duplex  requires  the  use  of  a  larger  battery 
than  the  differential  duplex. 


230 


ELECTRIC   LIGHTING. 


The  artificial  line. — An  ordinary  telegraph  line  has  not  only 
resistance  but  also  a  certain  amount  of  inductance,  and  there  is 
also  a  certain  electrostatic  capacity  between  the  line  and  the 
ground.  The  artificial  line  d  in  Figs.  138 
and  140  must  duplicate  the  properties  of 
the  real  line  in  every  respect  in  order  to 
completely  eliminate  the  effect  of  the  home 
battery  on  the  home  relay  in  Figs.  138  and 
140.  This  artificial  line  is  arranged  as 
shown  in  Fig.  141  in  which  r  and  r'  are 
adjustable  resistances,  C  is  a  condenser 
and  L  is  an  inductance.  This  arrange- 
ment does  not  enable  a  very  long  line  to  be  exactly  matched.* 

119.  Diplex  telegraphy. — The  sending  of  two  messages  (in  the 
same  direction)  over  one  line  wire  simultaneously  is  called 
diplex  telegraphy.  Diplex  telegraphy  depends  upon  the  use  of 


ground 

Fig.  141. 


Fig.  142.     Polarized  relay. 

*  Artificial  duplicates  of  very  long  lines  and  submarine  cables  are  described  in 
Maver's  American  Telegraphy,  pages  276  to  280. 


MISCELLANEOUS   APPLICATIONS. 


231 


two  kinds  of  relays,  namely,  (a)  An  ordinary  relay  with  a  fairly 
stiff  spring  so  that  the  lever  of  the  relay  responds  to  an  increase 
and  decrease  of  current,  the  current  being  never  reduced  to  zero; 
and  (b]  The  so-called  polarized  relay,  of  which  the  lever  responds 
to  reversals  of  current.  The  ordinary  relay  is  usually  called 
the  neutral  relay  to  distinguish  it  from  the  polarized  relay. 

The  polarized  relay. — A  general  view  of  a  polarized  relay  is 
shown  in  Fig.  142,  and  the  essential  features  of  the  relay  are 


Fig.  143. 


Fig.  144. 


shown  in  Figs.  143  and  144.  An  ordinary  electromagnet  (with 
soft  iron  cores)  is  mounted  on  one  pole  of  a  U-shaped  permanent 
magnet  of  steel,  and  a  light  iron  lever,  a  pivoted  at  p,  plays 
between  the  two  poles  NI  and  N2  of  the  electromagnet. 

When  current  flows  in  a  certain  direction  through  the  coils 
of  the  electromagnet  one  of  the  poles,  say  NI,  is  greatly 
strengthened  and  attracts  the  lever  a.  When  the  current  is 
reversed  the  other  pole  N2  is  strengthened  and  attracts  the 
lever  a.  Thus  the  lever  a  is  pulled  towards  NI  or  N2  accord- 
ing to  the  direction  of  the  current,  and  therefore  the  lever  a 
may  be  made  to  open  and  close  a  local  circuit  in  response  to 
reversals  of  the  line  current  which  flows  through  the  windings  on 
N  and  N%. 


232 


ELECTRIC   LIGHTING. 


Diplex  telegraphy. — Figure  145  shows  the  essential  features  of 
the  arrangements  for  diplex  telegraphy.  The  action  is  evident; 
the  polarized  relay  responds  to  the  reversing  key  R,  and  the 
neutral  relay  responds  to  the  increase-and-decrease  key,  J.  An 


home  station 


reversing 


increase  and 
decrease  key 


resistance 


line 


distant    station 
polarized      neutral 
relay          relay 


ground 


Fig.  145.     Diplex  telegraph. 


important  thing  which  is  not  shown  in  the  figure  is  that  the 
reversing  key  R  must  be  arranged  so  that  it  is  impossible  for 
the  operator  to  hold  its  lever  midway  between  the  contact  points, 
because  the  reversal  of  current  must  take  place  as  quickly  as 
possible  so  that  the  lever  of  the  neutral  relay  may  not  have  time 

to  respond.     The  lever  of  the  reversing 
key  is  therefore  usually  actuated  by  an 
electromagnet,   and    the    electromagnet 
*H"  is    controlled    by  a   hand-operated  key 

[         m which  opens  and  closes  the  local  circuit 

-=-  of  the  electromagnet.     Also  it  is  an  ad- 

'-=-  vantage  to  connect  condensers  as  shown 

in  Fig.  146  so  as  to  eliminate  sparking, 
and  to  ensure  the  quickest  possible  re- 
versal of  current.* 

A  neutral  relay  and  a  polarized  relay 
might  be  placed  in  circuit  with  a  diplex  line  at  a  way  station  so 

*  The  action  of  a  condenser  in  causing  a  quick  reversal  of  current  is  explained 
in  Franklin  and  MacNutt's  Electricity  and  Magnetism  (The  Macmillan  Co.);  see 
index. 


ground 

Fig.  146. 


MISCELLANEOUS   APPLICATIONS. 


233 


that  the  way  station  and  the  distant  end  station  could  both  re- 
ceive messages  from  the  sending  station.  This  arrangement, 
however,  is  never  used.  Indeed  diplex  telegraphy  is  used  only 
in  conjunction  with  duplex  telegraphy  to  give  quadruplex  teleg- 
raphy as  explained  in  the  next  article. 

120.  Quadruplex  telegraphy. — The  sending  of  four  messages 
(two  messages  each  way)  over  one  line  wire  simultaneously  is 

line 

" 

neutral  relay 

polarized  relay 


Fig.  147.     Bridge  Quadruplex. 

called  quadruplex  telegraphy.  This  is  accomplished  by  combining 
the  arrangements  for  duplex  (either  bridge  duplex  or  differential 
duplex)  and  diplex  telegraphy.  Thus  a  key  arrangement  like 
that  shown  in  Fig.  145  may  be  installed  at  each  station  in  Fig. 

^differential  polarized    relay 
r  V-  line 


differential  neutral  relay 


Fig.  148.     Differential  Quadruplex. 

138,  and  the  single  relay  at  each  station  in  Fig.  138  may  be  re- 
placed by  two  relays,  a  neutral  relay  and  a  polarized  relay,  as 
shown  in  Fig.  147.  The  local  circuits  and  sounders  are  omitted 
for  the  sake  of  clearness. 

Figure  148  shows  the  combination  of  the  diplex  and  the  dif- 


234  ELECTRIC   LIGHTING. 

ferential  duplex.  The  differential  duplex  has  an  advantage  over 
the  bridge  duplex  in  that  the  resistances  a  and  b  in  Figs.  138 
and  147  are  not  necessary  in  the  differential  system,  and  therefore 
it  is  possible  to  operate  the  differential  system  with  less  battery 
power. 

In  Figs.  147  and  148  the  neutral  relay  at  each  station  responds 
to  the  I  key  at  the  other  station,  and  the  polarized  relay  at  each 
station  responds  to  the  R  key  at  the  other  station. 

The  quadruplex  system  is  very  extensively  used  where  the  line 
wires  are  not  used  also  for  telephones  as  explained  in  Arts. 
129-135. 

Way  stations  cannot  be  served  in  the  quadruplex  system. 

121.  The  printing  telegraph*  is  an  arrangement  by  means  of 
which  a  simple  form  of  typewriter  is  operated  at  a  distant  station 
from  a  key  board  at  the  sending  station.  The  simplest  form  of 
printing  telegraph  is  the  well  known  ticker  which  prints  in  one 
line  on  a  long  strip  of  paper.  The  action  of  the  ticker  is  as 
follows:  Twenty-six  equidistant  pins  are  arranged  in  a  helical 
row  around  a  long  metal  cylinder.  This  cylinder  is  rotated  by  a 
small  electric  motor  or  by  clock  work,  and.  above  the  cylinder  is 
a  bank  of  twenty-six  lettered  keys  so  arranged  that  when  a  key 
is  depressed  one  of  the  pins  comes  against  it  and  the  cylinder 
is  stopped  in  a  certain  position;  the  next  key  would  stop  the 
cylinder  1/26  of  a  revolution  farther  on,  and  so  on.  Attached  to 
the  rotating  cylinder  is  a  device  for  reversing  an  electric  current 

*  The  ticker  as  now  generally  used  in  American  cities  is  somewhat  different  from 
the  device  here  described.  See  Maver's  American  Telegraphy,  pages  395-420. 

When  a  person  is  thoroughly  familiar  with  the  elements  which  enter  into  the 
construction  of  a  machine,  that  is,  when  a  person  is  familiar  with  shafts  and  wheels 
and  with  simple  devices  like  switches  for  opening  and  closing  circuits  and  for  re- 
versing connections,  a  more  easily  intelligible  description  of  a  complicated  machine 
can  be  made  without  illustrative  diagrams  and  drawings  than  can  be  made  with 
the  help  of  diagrams  and  drawings.  Indeed  it  would  be  confusing  under  the  speci- 
fied conditions  to  have  recourse,  even,  to  a  working  model  of  a  complicated  machine 
when  the  object  in  view  is  to  impart  a  clear  idea  of  its  fundamental  features.  The 
only  element  of  a  ticker  which  may  not  be  familiar  to  the  student  is  the  escapement 
device,  the  oscillations  of  which  turn  a  toothed  wheel  notch  by  notch. 


MISCELLANEOUS   APPLICATIONS.  235 

fifty-two  times  for  each  revolution  of  the  cylinder.  This  re- 
peatedly reversed  electric  current  passes  over  the  telegraph  line 
and  through  two  electromagnets  at  the  receiving  station.  One  of 
these  electromagnets  is  like  a  neutral  relay  with  a  heavy  lever,  and 
the  other  is  like  a  polarized  relay  with  a  light  lever  which  oscil- 
lates with  the  rapid  reversals  of  current  and  actuates  an  escape- 
ment which  turns  a  type  wheel  with  the  twenty-six  letters  ar- 
ranged around  its  periphery.  This  type  wheel  is  thus  turned 
step  by  step,  keeping  pace  with  the  rotating  cylinder  at  the 
sending  station.  When  the  cylinder  at  the  sending  station  is 
stopped  by  depressing  a  key,  the  A-key  for  example,  the  current- 
reversing  device  stops  also,  a  steady  current  flows  through  the 
line,  the  lever  of  the  polarized  relay  stops  oscillating,  the  type 
wheel  stops,  and  the  steady  current  excites  the  neutral  relay,  the 
lever  of  which  pushes  a  strip  of  paper  against  the  type  wheel  and 
prints  the  letter  A.  When  the  key  at  the  sending  station  is  raised 
the  current  reversals  begin  again,  the  type  wheel  at  the  receiving 
station  starts,  and  at  the  same  time  the  lever  of  the  neutral  relay 
falls  back  and  actuates  a  device  which  moves  the  strip  of  paper  a 
step  forward  for  the  printing  of  the  next  letter. 

122.  Submarine  telegraphy. — Figure  149  shows  a  full  size 
sectional  view  of  a  submarine  telegraph  cable.  The  conductor 
at  the  center  consists  of  a  number  of 
strands  of  copper  wire.  Surrounding 
this  is  a  layer  of  gutta  percha,  and  the 
whole  is  protected  by  a  covering  of 
tarred  hemp  and  steel  wire. 

The  conductor  and  metal  sheath  of 
the  cable,  together  with  the  intervening 
insulating  material,  constitute  a  con- 
denser of  large  electrostatic  capacity. 
The  effect*  of  this  large  electrostatic 
capacity  is  as  follows:  At  the  instant  a  battery  is  connected  to  a 

*  The  effect  which  is  here  described  is  exaggerated  by  the  action  of  the  inductance 
of  the  cable. 


236 


ELECTRIC   LIGHTING. 


Fig.  150. 


cable  a  very  large  current  begins  to  flow  into  the  cable.  Most  of 
this  current  goes  to  charge  the  cable,  and,  as  the  cable  becomes 
charged,  the  entering  current  falls  off  in  value,  settling  finally  to 

a  steady  value  which  is  de- 
termined by  the  resistance 
of  the  copper  wires  of  the 
cable.  The  ordinates  of 
curve  A,  Fig.  150,  show  the 
successive  values  of  current 
which  enters  a  cable  from 
a  battery,  the  abscissas 
being  time  reckoned  from 
the  instant  the  battery  is 
connected. 

At  the  distant  end  of 
the  cable  an  infinitesimal 
current  begins  to  flow  out 
of  the  cable  almost  at  the  instant  the  battery  is  connected 
to  the  cable  at  the  sending  station,  and  as  the  cable  be- 
comes charged  this  outflowing  current  rises  in  value  until  it 
reaches  a  steady  value  very  nearly  equal  to  the  steady  value  of 
the  entering  current.  The 
curve  B,  Fig.  150,  shows 
the  growth  of  current  flow- 
ing out  of  the  distant  end 
of  a  cable  after  a  battery 
is  connected  to  the  near 
end.  When  the  battery  is 
disconnected,  the  entering 
current  ceases  at  once,  but 
the  outflowing  current  at 
the  distant  end  of  the  ca- 
ble drops  slowly  to  zero  as 
the  accumulated  charge  flows  out  of  the  cable. 

Distortion  of  current  pulses  by  a  cable. — The  curve  a,   Fig.  151, 
shows  the  character  of  the  current  pulse  which  enters  a  cable 


elapsed  time 


elapsed  time 

Fig.  151. 


MISCELLANEOUS   APPLICATIONS.  237 

when  a  battery  is  momentarily  connected  to  the  cable,  and  the 
curve,  b,  shows  the  character  of  the  current  pulse  which  flows 
out  of  the  distant  end  of  the  cable.  The  action  of  a  cable  in 
thus  altering  the  character  of  a  current  pulse  is  called  distortion. 
Land  lines  distort  current  pulses  to  some  extent,  and  it  is  for 
this  reason  that  a  very  long  telegraph  line  cannot  be  satisfactorily 
operated  as  a  single  circuit.  Distortion  very  seriously  impairs 
the  distinctness  of  telephonic  transmission  in  land  lines  four  or 
five  hundred  miles  long  or  more.* 

The  distortion  of  electric  current  pulses  by  a  submarine  cable 
is  analogous  to  the  distortion  of  water-current  pulses  by  a  long 
thin-walled  rubber  tube.  If  water  is  forced  into  one  end  of  such 
a  tube  in  sharply  denned  pulses,  the  water  will  flow  out  of  the 
other  end  of  the  tube  in  one  long  continued  pulse,  and  a  succession 
of  separate  pulses  of  inflowing  water  would  show  themselves  as 
slight  variations  of  outflowing  current. 

The  curves  aaaa,  Fig.  152,  represent  four  short  current  pulses 
sent  into  a  cable  at  one  end,  and  the  curve  b  represents  the  pulse 
of  current  which  flows  out  of  the 
cable  at  the  other  end.  The  four 

success've    pulses    of    inflowing 

,  .  elapsed  time 

current  show  themselves  as  four 

slight  humps  on  the  curve  b 
of  outflowing  current,  and  it  is 
evident  that  these  four  success- 
ive pulses  of  inflowing  current 

elapsed   time 

could  not  be  detected  by  means  Fig  152 

of  an  ordinary  relay  and  sounder 

at  the  distant  end  of  the  cable.  The  receiving  instrument  in  sub- 
marine telegraphy  is  a  galvanometer  arranged  to  trace  the  curve 
of  outflowing  current  at  the  receiving  end  of  the  cable,  and  the 
separate  current  pulses  that  are  sent  into  the  cable  at  the  sending 

*Wave  distortion  is  very  fully  and  simply  discussed  on  pages  29,  30,  108-115 
of  Franklin's  Electric  Waves. 


238  ELECTRIC   LIGHTING. 

end  are  inferred  from  the  slight  humps  in  the  curve  which  is 
traced  by  the  receiving  instrument. 

123.  The  syphon  recorder.* — The  receiving  instrument  com- 
monly used  in  submarine  telegraphy  is  called  the  syphon  recorder. 
The  current  flowing  out  of  the  distant  end  of  a  cable  passes 
through  a  D'Arsonval  galvanometer,  the  moving  coil  of  which 
produces  sidewise  motion  of  a  pen  which  traces  an  ink  line  on  a 
moving  strip  of  paper;  the  pen  thus  traces  a  current  curve  like  b, 
Fig.  152. 

124.  The  telephone. — The  telephone  set  includes  a  transmitter, 
a  receiver,  and  an  arrangement  for  calling.     The  transmitter  is  a 
device  for  producing  over  the  line  a  current  which  is  reversed 
with  each  to  and  fro  movement  of  a  diaphragm,  the  diaphragm 
being  set  into  vibration  by  a  speaker's  voice ;  and  the  receiver  is  a 
device  in  which  a  diaphragm  is  set  into  vibration  by  these  rapidly 
reversed  currents  (which  come  to  it  over  the  line  from  the  trans- 
mitter) thus  reproducing  the  original  sound. 

The  transmitter. — A  sectional  view  of  a  telephone  transmitter 
is  shown  in  Fig.  153,  and  the  connections  are  shown  in  Fig.  155. 
An  electric  circuit  contains  a  battery,  the  primary  of  a  small 
transformer  (induction  coil),  and  a  mass  of  granular  carbon 

*  The  syphon  recorder  was  devised  by  Lord  Kelvin,  who  contributed  more, 
perhaps,  to  the  development  of  transatlantic  telegraphy  than  any  other  man.  In 
an  article  by  Professor  W.  E.  Ayrton,  which  appeared  in  the  London  Times  shortly 
after  Lord  Kelvin's  death  (reprinted  in  Popular  Science  Monthly  for  March,  1908), 
much  interesting  information  is  given  concerning  what  Kelvin  did  for  submarine 
telegraphy.  "When  signals  through  the  1858  Atlantic  cable  became  weak,  and  a 
message  from  the  President  to  our  Queen  took  thirty  hours  in  transmission  although 
containing  only  150  words,  and  which  would  need  only  three  or  four  minutes  to 
transmit  through  any  one  of  our  good  Atlantic  cables  of  to-day,  the  only  remedy  of 
those  who  looked  down  upon  the  theories  of  the  young  Glasglow  professor  was  to 
use  Whitehouse's  "thunder  pump,"  a  magneto-electric  machine  which  produced 
a  sudden  large  electromotive  force  when  the  armature  of  a  permanent  magnet  was 
jerked  off  the  poles  of  the  magnet.  But  these  shocks  only  sent  sparks  through  the 
gutta-percha  insulating  coating  and  hurried  the  poor  cable  to  its  doom,  so  that 
even  the  three  words  per  minute  which  would  have  been  the  utmost  limit  of  speed 
possible  had  this  cable  been  entirely  uninjured,  were  replaced  by  absolute  silence." 


MISCELLANEOUS   APPLICATIONS. 


239 


between  corrugated  carbon  blocks,  all  in  series.  The  black 
patches  in  Fig.  153  represent  the  carbon  blocks,  one  of  which  is 
supported  rigidly,  a/id  the  other  of  which  is  attached  to  the 
diaphragm  DD.  The  speak- 
er's voice  causes  the  dia- 
phragm to  vibrate  and  the 
resistance  of  the  granular 
carbon  increases  and  de- 
creases as  the  diaphragm 
moves  to  and  fro.  This 
variation  of  resistance 
causes  the  battery  current 
to  increase  and  decrease, 
and  this  increase  and  de- 
crease of  battery  current  in 


Fig.  153. 


the  primary  of  the  small  transformer  produces  in  the  second- 
ary a  current  which  flows  in  one  direction  and  the  other  alter- 
nately as  the  diaphragm  moves  to  and  fro. 

The  receiver. — The  simplest  type  of  telephone  receiver  is  shown 
in  Fig.  154.     A  coil  of  very  fine  wire,    C,    is  wound  around  one 

end  of  a  permanent  steel 
magnet  MM,  and  the 
reversals  of  current  from 
the  distant  transmitter  in 
flowing  through  this  coil 
strengthen  and  weaken 
the  steel  magnet  alter- 
nately, and  the  thin  iron 
diaphragm  dd  is  moved  to  and  fro  by  the  variations  of  strength 
of  the  steel  magnet,  thus  reproducing  the  original  sound.  The 
most  approved  form  of  telephone  receiver  has  a  bi-polar 
magnet. 

Two  telephone  stations  all  connected  up  for  talking  are  shown 
in  Fig.  155.     In  order  to  give  a  call  at  the  distant  station  a  small 


Fig.  154. 


240 


ELECTRIC   LIGHTING. 


magneto  generator  is  used  to  operate  a  bell,*  and  the  change 
from  connections  required  to  operate  the  bell  to  connections  re- 
quired for  the  operation  of  transmitter  and  receiver  is  made  by 

receiver 


&~ 

transmittcr 

-^ 

induction  coil 
or  transformer 


•ground 


ground 


Fig.  155. 


the  movement  of  the  hook  when  the  telephone  is  taken  from  the 
hook.  Figure  156  shows  the  hook  down,  and  the  connections, 
as  indicated  by  the  full  lines  (dotted  lines  are  dead) ,  are  proper 


receiver 


transmitter 


line 


honk 


Fig.  156.     Connections  for  ringing. 

for  operating  the  bell  at  the  distant  station.  Figure  157  snows 
the  hook  up,  and  the  connections  are  proper  for  operating  the 
transmitters  and  receivers. 

*Let  it  be  understood  that  we  are  not  discussing  central  exchange  telephone 
systems,  but  simple  two-station  telephone  lines  such  as  are  extensively  used  in 
railway  work.  The  student  is  referred  to  Kempster  B.  Miller's  American  Telephone 
Practice  for  full  information  on  telephone  practice. 


receiver 


MISCELLANEOUS   APPLICATIONS. 
line 


transmitter 


hook 


line 


Fig.  157.     Connections  for  talking. 

125.  The  ground  return  versus  the  metallic  circuit. — Many 
private  and  railway  telephone  lines  use  a  single  wire  with  ground 
return.     Such  lines  are  objectionable  for  two  reasons,  namely, 
(a)  The  atmospheric  electricity  gathered  by  such  a  line  flows 
to  ground  through  the  telephone  receivers  and  makes  an  almost 
incessant  crackling  sound  which  is  very  annoying;  and  (b)  It  is 
impossible  in  the  case  of  such  a  line  to  eliminate  the  disturbances 
due  to  adjacent  electric  light  and  power  lines.     First  class  tele- 
phone service  demands  therefore  a  wire  circuit  (two  wires),  and 
such  a  telephone  line  is  called  a  metallic  circuit.     The 
advantages  of  the  metallic  circuit  are  (a)  That  disturb- 
ances can  be  more  completely  eliminated  when  two 

wires  are  used,  and  (b)  A  two-wire  line  lends  itself 
more  readily  than  a  single-wire  line  to  combination 
uses  as  explained  later  in  connection  with  simplex, 
composite  and  phantom  circuits. 

126.  The  use  of  divided  choke-coils  on  metallic 
telephone  circuits. — A  divided   choke-coil  is  a  con- 
tinuous winding  of  wire  on  an  iron  core  with  a  lead    — * 
wire  brought  out  from  the  middle  of  the  winding,  as 

shown  in  Fig.  158.  There  is  great  inductive  opposition  to  the  flow 
of  alternating  current  through  the  entire  coil,  but  equal  alternating 
currents  can  enter  at  a  and  c  and  flow  out  at  b  without  induc- 


242  ELECTRIC   LIGHTING. 

live  opposition  because  the  magnetizing  action  of  one  half  of  the 
winding  is  neutralized  by  the  opposite  magnetizing  action  of  the 
other  half  of  the  winding. 

Figure  159  shows  a  metallic  telephone  circuit  (the  telephone 
sets  being  like  those  shown  in  Figs.  156  and  157)  with  a  divided 

telephone  set  line  telephone  set  ^ 

m 


divided  choke  coil  divided  choke 

line 


-=--  ground  ground 

Fig.  159. 

choke-coil  connected  between  the  line  wires  at  each  end  of  the 
line,  the  middle  lead  of  each  choke-coil  being  connected  to  earth. 
The  high  frequency  telephone  currents  cannot  flow  through  the 
choke-coils  to  any  appreciable  extent,  but  any  current  (alternating 
or  direct)  which  flows  in  the  same  direction  in  both  line  wires  can 
flow  without  inductive  opposition  through  the  two  halves  of  a  choke- 
coil  and  to  ground  without  affecting  the  telephones. 

Thus  the  atmospheric  electricity  which  gathers  equally  on  the 
two  line  wires  has  an  easy  path  to  earth  without  flowing  through 
either  telephone,  and  any  current  which  is  induced  equally  and 
in  the  same  direction  in  the  two  line  wires  has  an  easy  path  to 
ground  without  flowing  through  either  telephone. 

A 

/"•-• 
telephone 


ground  ground 

Fig.  160. 

Figure  160  shows  a  metallic  telephone  circuit  in  which  the  high 
frequency  telephone  currents  are  delivered  to  the  line  (and  from 
the  line)  by  two  small  transformers  A  and  B;  and  the  trans- 
former coils  which  are  connected  to  the  line  have  their  middle 


MISCELLANEOUS   APPLICATIONS. 


243 


points  grounded.  This  arrangement  is  equivalent  to  the  arrange- 
ment shown  in  Fig.  159.  The  small  transformers  A  and  B 
in  Fig.  1 60  with  the,  lead  coming  out  of  the  middle  of  one  of  their 
coils  are  called  divided  repeating  coils 

127.  The  phantom  telephone  circuit. — Two  metallic  telephone 
circuits  like  Fig.  159  (or  like  Fig.  160)  can  be  used  as  telephone 
circuits  and  at  the  same  time  a  third  telephone  circuit  can  be 
established  as  indicated  in  Fig.  161,  in  which  A  A'  is  one  set  of 
telephones  like  Fig.  159,  BBf  is  another  set  of  telephones  like 


H 

!«  a'  f 

n  r  n 

u. 

c^=4 

|c                                                                                         cr| 
"^^  ground                           k                     ground  -°4?~ 

>c- 

H 

p  u 

s  6  ^fc'  6'  1 

—      r> 

Fig.  161. 

159,  and  CCf  is  a  third  set  of  telephones,  all  of  which  operate 
independently  of  each  other.  Telephone  current  (high  frequency 
alternating)  from  C  cannot  flow  across  the  choke-coil  c  but 
can  enter  the  two  wires  /  and  /'  through  the  two  halves  of  choke- 
coil  a,  flow  through  the  telephone  set  Cf  and  return  through  the 
two  wires  k  and  k'.  This  circuit  is  called  the  phantom  circuit: 

128.  The  choke-coil  and  the  condenser. — The  simultaneous  use" 
of  wires  for  Morse  telegraph  and  for  telephone  depends  in  part 
upon  the  use  of  choke-coils  and  in  part  upon  the  use  of  con- 
densers; and  it  is  important  to  understand  that  high  frequency 
alternating  current  cannot  flow  through  a  choke-coil  but  can 
flow  freely  through  a  condenser,  whereas  a  very  low  frequency 
alternating  current  or  a  direct  current  can  flow  freely  through 
a  choke-coil  but  cannot  flow  through  a  condenser. 

If  the  main  rod  in  Fig.  162  oscillates  back  and  forth  at  high 
frequency  the  heavy  weight  does  not  move  perceptibly,  but  all 


244 


ELECTRIC   LIGHTING. 


of  the  motion  of  the  main  rod  is  accommodated  by  motion  of  the 
end  C  of  the  lever  CL.  If  the  main  rod  oscillates  back  and 
forth  at  very  low  frequency  the  end  C  of  the  lever  does  not  move 

spring 


Fig.  162. 

perceptibly,  but  all  of  the  motion  of  the  main  rod  is  accommo- 
dated by  motion  of  the  end  L  of  the  lever.  If  any  agent  A 
causes  the  main  rod  to  oscillate  back  and  forth  at  high  frequency 
and  if  another  agent  B  causes  the  main  rod  to  move  back  and 
forth  at  low  frequency  the  two  motions  are  added  together  so  far 
as  the  main  rod  is  concerned,  that  is  the  mam  rod  performs  both 
motions  simultaneously,  but  the  end  C  of  the  lever  will  move 
as  if  agent  A  were  acting  alone  and  the  end  L  of  the  lever  will 
move  as  if  agent  B  were  acting  alone;  indeed,  end  C  of  the 
lever  will  respond  to  agent  A  and  end  L  of  the  lever  will 
respond  to  agent  B. 


main  line 

C 

• 

capacity 

i 
ground    return 

L 

or 

I 

ooo  (ToTo  000  O'O  0 

inductance 
wire    return                             j 

Fig.  163. 


In  action  the  mechanical  arrangement  in  Fig.  162  is  exactly 
analogous  to  the  electrical  arrangement  in  Fig.  163.  If  one  agent 
A  produces  a  high  frequency  alternating  current  through  the 


MISCELLANEOUS   APPLICATIONS. 


245 


circuit  ////  and  if  another  agent  B  produces  at  the  same  time 
a  low  frequency  alternating  current  through  the  circuit,  then  the 
high  frequency  current  produced  by  A  will  flow  through  the 
condenser  (capacity)  and  the  low  frequency  current  produced  by 
B  will  flow  through  the  inductance. 

129.  The  railway  composite. — The  arrangement  for  using  an 
ordinary  ground-return  telegraph  line  for  telephone  service  at 
the  same  time  that  it  is  being  used  for  telegraph  service  is  called 
the  railway  or  one-wire  composite.  Such  an  arrangement  with 
a  way  station  served  both  by  telegraph  and  telephone  is  shown  in 
Fig.  164.*  The  high  frequency  telephone  currents  and  the  low 
frequency  telegraph  currents  flow  together  over  the  line  and 


condenser 


Cation  A 


choke 
coil 


relay  Q 
fa*T 


station  B 


condenser 


telephone 
-^  se^ 


ooooo     _ 

choke    relay     key 
coil 
way  station 


i 


ground 


Fig.  164.     The  railway  composite. 


return  through  the  ground,  but  the  telephone  currents,  only, 
flow  through  the  condensers  and  telephones,  and  the  telegraph 
currents,  only,  flow  through  the  choke-coils,  relays  and  keys 
(which  are  of  course  all  closed  but  one). 

The  arrangement  shown  in  Fig.  164  is  not  very  satisfactory 
because  a  number  of  telephone  sets  do  not  operate  satisfactorily 
in  series.  It  is  better  to  connect  the  telephones  all  from  line  to 


*  The  telephone  calls  are  usually  made  by  means  of  the  telegraph.     See  Art.  137. 


1 


246  ELECTRIC   LIGHTING. 

ground  so  that  any  transmitter  supplies  current  to  all  of  the 
receivers  in  parallel.  This  arrangement,  which  is  shown  in  Fig. 
165,  allows  all  of  the  telegraph  relays  to  be  operated  in  series  and 

choke    ret,...  ,  at  the  same  time  it  allows  any 

coil      r~^  key 

— WffWffffinrxJ — * — )          telephone  transmitter  to  deliver 

— 1  lin-Z    current  at  all  of  the  telephone 

receivers  in  parallel. 

The  excessively  quick  change 
of  current  due  to  the  opening 
and  closing  of  a  telegraph  key 

telephone  causes  a  momentary  flow  of  cur- 

rent through  the  condensers  and 
^  telephones  so  that  the  telegraph 

signals  are  audible  in  the  tele- 
Fig.  165. 

phones.      This   difficulty    is    to 

a  great  extent  obviated  by  "bridging"  a  condenser  across  each 
key  or  across  each  key  and  relay  taken  together,  as  shown  in 
Figs.  1 68  and  169.  Each  relay  should  also  be  shunted  by  a  non- 
"inductive  high  resistance  so  as  to  eliminate  high  frequency  oscil- 
lations around  the  circuit  which  is  formed  at  each  station  by  the 
telephone  and  telegraph  apparatus  (at  the  way  station  by  the 
telegraph  apparatus  and  the  condenser  C  in  Fig.  165).  Of 
course  the  relays  are  themselves  choke-coils  and  in  some  cases 
therefore  the  additional  choke-coils  shown  in  Figs.  164  and  165 
might  be  omitted. 

130.  The  simplex  circuit. — The  railway  composite  is  useful 
but  it  has  all  of  the  disadvantages  of  a  ground-return  telephone 
line  (see  Art.  125)  and  the  telegraph  signals  cannot  be  entirely 
eliminated  from  the  telephones.  An  arrangement  in  which  these 
objectionable  features  are  avoided  is  the  simplex  circuit  which 
is  shown  in  Fig.  166.  The  action  of  this  arrangement  may  be 
understood  with  the  help  of  the  discussion  of  Arts.  126  and  127. 
The  two  wires  of  the  metallic  telephone  circuit  serve  as  one  wire 
for  a  ground-return  telegraph  circuit,  and,  if  there  are  no  way 


MISCELLANEOUS  APPLICATIONS.  247 

stations,  this  telegraph  circuit  can  be  operated  duplex  or  quadru- 
plex by  installing  apparatus  like  Figs.  147  or  148  for  the  simple 
telegraph  apparatus  shown  in  Fig.  166. 

^telephone  set 


n 


L 

r~ 


relay 

battery 

ground 

Fig.  166.     The  simplex  telegraph  circuit. 

Figure  167  shows  a  simplex  circuit  with  a  telegraph  set  at  a 
way  station.  The  way  station  may  also  be  served  by  a  telephone, 
the  telephone  set*  being  connected  across  ("bridged"  across) 
between  the  two  wires  on  either  side  of  the  condensers  in  Fig.  167. 

131.  The  simplex  on  phantom. — Telegraph  apparatus  can  be 
inserted  in  the  two  ground  leads  in  Fig.  161,  thus  giving  three 
metallic  telephone  circuits  and  one  ground-return  telegraph  cir- 
cuit on  four  wires. 

Duplex  or  quadruplex  apparatus  like  Figs.  147  or  148  can  be 
inserted  in  the  ground  leads  in  Fig.  161,  thus  giving  three  inde- 
pendent metallic  telephone  circuits  and  permitting  the  sending 

-rc —          j  B  t. : — TL 

r* 


relay 


Fig.  167.     Telegraph  way  station  on  simplex. 

of  four  telegraph  messages  over  the  four  wires  of  Fig.  161  all  at 
the  same  time.  The  matter  of  duplex  and  quadruplex  working 
on  telephone  lines  is  discussed  briefly  from  a  practical  point  of 
view  in  Art.  138. 

*  The  magneto  and  bell  are  not  shown  in  Figs.  166  and  167.     See  discussion  of 
telephone  calls  in  Art.  137. 


h               i* 

L=J 

r=i  . 

n                          r! 

248 


ELECTRIC   LIGHTING. 


132.  Phantom  on  two  simplex  circuits. — A  phantom  telephone 
circuit  may  be  superposed  upon  two  simplex  circuits  like  Fig.  166. 
This  arrangement  is  shown  in  Fig.  1 68.  Theoretically  both  of 


H 

1  —  • 

H 

h' 

cH   " 

P                                                                            Ijyl 

L,c' 

choke 

coil 

relay 

ke 


w 


•*&•  ground  ""f5" 

Fig.  168.     Telephone  phantom  on  two  simplex  circuits. 

the  telegraph  circuits  in  Fig.   168  can  be  operated  duplex  or 
quadruplex.     See  Art.  138. 

133.  The  two- wire  composite  circuit. — A  metallic  telephone 
circuit  making  use  of  two  ordinary  ground-return  telegraph  lines 
is  called  a  two-wire  composite  circuit.     Such  an  arrangement  is 
shown  in  Fig.  169. 

134.  Phantom  on  two  two-wire  composites. — A  phantom  tele- 
phone circuit  may  be  superposed  upon  two  two-wire  composite 
circuits  as  shown  in  Fig.  170. 

135.  Simplex  blocks  worked  in  series  for  telegraph. — A  num- 
ber of  metallic  telephone  circuits  such  as  are  used  for  communicat- 
ing between  signal  stations  on  a  railway  can  be  connected  for  use 


MISCELLANEOUS   APPLICATIONS. 


249 


ground 


I    coi/ 


*^p"  ground  -^^ 

Fig.  169.     Two-wire  composite. 


m- 


H^ 


* 


=nd 


^o 

H    f=^ 


Fig.  170.     Telephone  phantom  on  two  two-wire  composites. 


250 


ELECTRIC   LIGHTING. 


as  a  long  telegraph  line  as  shown  in  Fig.  171,  and  the  telegraph 
circuit  can  be  carried  onwards  as  a  single-wire  line  as  shown  in 
Fig.  172. 

block  A  block   B 


block  C 


H 

n 

s 

jj 

rn 

s                g 

n  P 

rn 

h    rf 

r 

relayQ 
key} 

1                                                 f              "\                                             /  '             / 

e/a^ 
?!/ 

T 

ikt 

ground  ground 

Fig.  171.     Simplex  blocks  in  series  for  telegraph. 

136.  Way  stations  in  general. — In  the  simple  Morse  telegraph 
a  number  of  way  stations  can  be  arranged,  the  relays  and  keys 
being  all  in  series.  Five  or  six  way  stations  can  also  be  arranged 
on  a  telephone  line  (metallic  circuit  or  ground-return) ;  in  this 
case  it  is  best  to  use  telephone  receivers  and  call  bells  wound 
with  many  turns  of  fine  wire  and  to  connect  the  telephone  set  at 


block  C 


extension  of  telegraph  circuit 


-=• 


ground 
Fig.  172.     Extension  of  telegraph  circuit  of  Fig.  171. 

each  station  between  the  two  wires  of  the  line  or  between  the 
single  line  wire  and  the  ground.  That  is,  all  of  the  telephone 
sets  are  in  parallel. 

Way  stations  cannot  be  arranged  in  duplex  or  quadruplex 
systems. 


MISCELLANEOUS   APPLICATIONS.  251 

In  simplex  circuits  and  composite  circuits  telegraph  way  sta- 
tions may  be  arranged  by  breaking  the  telegraph  circuit*  with  a 
condenser  and  shunting  the  telegraph  set  and  a  choke-coil  around 
the  condenser. 

In  simplex  circuits  and  composite  circuits  telephone  way  sta- 
tions may  be  arranged  either  by  shunting  the  telephone  appa- 
ratus (with  a  condenser)  around  the  telegraph  apparatus  (with 
a  choke-coil),  or  by  connecting  the  telephone  apparatus  (with 
a  condenser)  between  the  two  wires  or  legs  of  the  telephone 
circuit. 

137.  Telephone  calls. — The  ordinary  magneto  generator  which 
is  used  for  operating  telephone  call  bells  gives  an  alternating 
current  of  which  the  frequency  is  about  16  cycles  per  second,  and 
a  one  or  two  microfarad  condenser  is  a  very  great  obstruction  to 
the  flow  of  such  low-frequency  alternating  current.  Therefore 
the  ordinary  magneto  and  bell  cannot  be  used  for  making  tele- 
phone calls  on  composite  circuits  such  as  are  shown  in  Figs.  164, 
169  and  170.  Telephone  calls  are  frequently  made  on  composite 
circuits  by  a  momentary  use  of  the  telegraph  apparatus.  An- 
other arrangement  is  to  use  a  small  induction  coil  with  a  high- 
frequency  interrupter  for  producing  moderately  high-frequency 
alternating  current  for  calling.  These  high-frequency  currents 
can  flow  through  the  condensers  and  operate  a  bell  which  is 
specially  designed  to  be  operated  by  high-frequency  current, 
or  the  telephone  receiver  can  be  left  permanently  in  circuit  in 
which  case  the  high-frequency  current  will  produce  a  loud  howling 
sound  in  the  telephone  receiver.  This  latter  arrangement  is 
called  the  howler  call. 

The  divided  choke-coils  (or  the  divided  repeating  coils)  which 
are  used  in  the  simplex  circuit  can  be  made  large  enough  to 
obstruct  the  flow  of  the  i6-cycle  bell  current  without  hindering 
the  telegraph  current  and  therefore  the  ordinary  magneto  and 
bell  can  be  used  on  simplex  circuits. 

*  If  a  pair  of  wires  forms  one  side  of  the  telegraph  circuit  both  wires  must  be 
broken  as  stated.  See  Fig.  167. 


252  ELECTRIC    LIGHTING. 

138.  Duplex  and  quadruplex  on  simplex  and  composite  cir- 
cuits.— There  are  two  difficulties  involved  in  the  use  of  duplex 
and  quadruplex  telegraph  apparatus  or  simplex  and  composite 
circuits,  namely,  (a)  the  complexity  is  such  that  the  balanced 
condition  between  the  "line"  and  the  "artificial  line"  is  difficult 
to  maintain,  even  to  a  degree  sufficient  to  keep  the  different 
telegraph  signals  separated,  and  (b)  large  voltages  (sometimes 
150  volts  or  more)  and  heavy  currents  are  required,  especially 
for  quadruplex  working,  and  the  telegraph  signals  are  usually 
heard  in  the  telephones.     //  is  essential  to  keep  the  telegraph  current 
as  low  as  possible  in  simplex  and  composite  circuits.     Therefore 
the  quadruplex  is  practically  abandoned  on  such  circuits. 

139.  The    automatic    railway    block    signal. — When    railway 
trains  are  run  closely  following  each  other  it  is  quite  necessary  to 
install  a  system  of  signals  to  show  to  the  engineer  that  he  has 
a  mile  or  two  of  clear  track  ahead,  the  signal  system  being  so 
designed  that  the  presence  of  a  train  ahead  or  any  chance  derange- 
ment of  the  apparatus  will  show  a  danger  signal. 

rail  A 


1 

i 

\ 

1 

|                 na  B               bond? 
%  battery 

HUP                                    relaa 

7 

Fig.  173.     Short  railway  block  with  single-arm  semaphore. 

The  essential  features  of  the  block  signal  system  are  shown  in 
Fig.  173.  The  rails  of  a  block  are  separated  from  the  rails  of  the 
adjoining  blocks  by  insulating  joints  iiii,  and  the  rails  in  the 
block  are  connected  together  by  wire  bonds  so  as  to  make  each 
rail  a  continuous  conductor.  A  battery  with  some  resistance  r 
in  series  with  it*  is  connected  between  the  rails  at  one  end  of 
the  block,  and  the  windings  of  a  relay  are  connected  between 

*  Gravity  Daniell  cells  are  generally  used,  and  the  internal  resistance  of  such  a 
battery  is  usually  sufficient  without  the  insertion  of  any  additional  resistance  r. 


MISCELLANEOUS   APPLICATIONS.  253 

the  rails  at  the  other  end  of  the  block.  The  battery  current  thus 
flows  steadily  through  the  relay,  and  the  signal  arms  are  held  in 
the  position  which  shows  that  the  track  is  clear.  When  a  train 
comes  into  the  block  the  wheels  and  axles  of  the  train  make  a 
short-circuit  connection  from  rail  to  rail,  and  the  voltage  between 
the  rails  falls  to  zero  so  that  no  perceptible  current  flows  through 
the  relay.  The  relay  lever  is  therefore  released  and  allowed  to 
fall  back,  a  local  circuit  is  opened  and  the  signal  arms  move  to  the 
"danger"  position.  It  is  of  the  utmost  importance  that  the  danger 
signal  be  displayed  when  any  derangement  of  the  signal  apparatus 
occurs;  therefore  the  arms  of  the  semaphore  are  weighted  so  as 
to  fall  to  "danger"  position  when  the  local  circuit  is  opened 
either  by  the  track  relay  or  by  accident. 

When  the  train  moves  out  of  the  block,  current  again  flows 
through  the  relay,  the  local  circuit  is  closed  and  a  small  motor  in 
the  local  circuit  moves  the  signal  arms  to  the  "safe"  position. 
Copper  oxide  cells  are  extensively  used  for  the  local  circuits  for 
operating  the  small  motors  for  moving  the  signal  arms. 


1 

y 

•-mWs 

TT 

Fig.  174.     Arrangement  for  working  very  long  section  of  track  as  a  single  block. 

There  is  always  considerable  leakage  of  current  across  from  rail 
to  rail  in  Fig.  173  through  the  ties  and  ballast,  especially  when  the 
road  bed  is  wet,  and  because  of  this  leakage  of  current  a  relay 
connected  as  shown  in  Fig.  173  does  not  operate  satisfactorily  if 
the  block  is  more  than  6,000  or  7,000  feet  in  length.  When  the 
traffic  on  a  railway  is  light  it  is  desirable  to  have  blocks  two  or 
three  or  four  miles  in  length,  and  blocks  of  this  length  can  be 
arranged  as  shown  in  Fig.  174.  Relay  A  controls  the  motor 
which  moves  the  signal  arm,  and  relay  B  makes  the  two  sections 


254 


ELECTRIC   LIGHTING. 


operate  as  one  block.  When  both  sections  are  clear,  battery  b 
energizes  relay  B  and  the  lever  of  relay  B  connects  battery  a 
to  the  rails  of  section  A  so  that  relay  A  is  energized  and  the 
signal  arm  is  held  at  "safe"  position.  A  train  on  either  section 
causes  the  current  to  cease  flowing  through  relay  A  and  the 
signal  arm  falls  to  "danger." 

140.  The  overlap  track  circuit. — A  system  of  signals  which  is 
extensively  used  is  as  follows:  A  locomotive  engineer  brings  a 
train  up  to  the  entrance  to  a  new  block,  and  if  he  sees  both  arms 
of  a  double  semaphore  at  "safe"  he  knows  the  entire  block  is 
clear;  if  he  sees  one  arm  at  "safe"  and  the  other  at  "danger" 
he  knows  that  a  train  is  on  the  distant  half  of  the  block,  and  if 


A                                              B 

J 

«*^_  . 

J 

relay  A  relaV  B 

Fig.  175.     Arrangement  for  operating  double-arm  semaphore. 

he  sees  both  arms  at  "danger"  he  knows  that  a  train  is  on  the 
adjacent  half  of  the  block.  In  the  first  case  the  engineer  goes 
ahead  at  full  speed,  in  the  second  case  the  engineer  goes  ahead 
cautiously  at  reduced  speed,  and  in  the  third  case  the  engineer 
stops  the  train  until  the  signals  show  that  the  first  half  of  the 
block  is  clear. 

Figure  1 75  shows  an  arrangement  for  operating  a  double  sema- 
phore as  above  explained.  When  the  train  is  on  section  B  both 
relays  are  without  current  and  both  semaphore  arms  (at  P)  are 
at  "danger."  When  the  train  moves  into  section  A,  relay  B 
is  energized  and  one  semaphore  arm  (at  P)  is  moved  to  "safe" 
position,  and  when  the  train  moves  out  of  section  A  both  relays 
are  energized  and  both  semaphore  arms  (at  P)  move  to  "safe" 


MISCELLANEOUS   APPLICATIONS.  255 

position.     The  arrangement  shown  in  Fig.    176  is  called  the 
overlap  track  circuit.* 

- 

REFERENCES. 
Fire  alarm  and  police  telegraphy: 

Maver's  American  Telegraphy,  J.  H.  Bunnell  &  Co.,  1892 

Wireless  telegraphy: 

Poincare-Vreeland,   Maxwell's   Theory  and   Wireless   Telegraphy,   McGraw-Hill 

Book  Co.,  1904. 
J.  A.  Fleming,  The  Principles  of  Wireless  Telegraphy,  Longmans,  Green  &  Co., 

1908. 
G.  W.  Pierce,  The  Principles  of  Wireless  Telegraphy,  McGraw-Hill  Book  Co., 

1910. 

Electric  furnace  work: 

J.  B.  Kershaw,  The  Electric  Furnace  in  Iron  and  Steel  Production,  Van  Nostrand, 

1907. 

Rodenhauser  &  Schoenawa,  Electrische  Of  en  in  der  Eisenindustrie,  Leipzig,  1911. 
J.  Bronn,  Electrische  Ofen  im  Dienste  der  keramischen  Gewerbe  und  der  Glas  und 

Quarzglasererzeugung,  Halle,  1910. 

Borchers-Solomon,  Electric  Furnaces,  Longmans,  Green  &  Co.,  1908. 
A.  Neuburger,  Handbuch  der  praktischen  Electrometallurgie,  Berlin,  1907. 
J.  B.  Kershaw,  Electrometallurgy,  Van  Nostrand,  1908. 
M.  deKay  Thompson,  Applied  Electrochemistry,  The  Macmillan  Co.,  1911. 

Protection  of  buildings  from  lightning: 

Oliver  J.  Lodge,  Lightning  Conductors  and  Lightning  Guards,  London,  1892. 

Electric  welding: 

R.  N.  Hart,  Welding,  McGraw-Hill  Book  Co.,  1910. 

Ore  concentration: 

C.  G.  Gunther,  Electromagnetic  Ore  Separation,  McGraw-Hill  Book  Co.,  1909. 

Ozone: 

F.  M.  Per  kin,  The  Industrial  Uses  of  Ozone,  Nature,  February  22,  1912. 
A  good  discussion  of  the  manufacture  and  use  of  ozone  is  given  in  Bulletin  No.  4912 

of  the  General  Electric  Company. 
M.  W.  Franklin,  Ozone  ;  Its  Properties  and  Commercial  Production,  Proceedings 

American  Institute  of  Electrical  Engineers,  May.  1812,  pages  597-6<>7. 

*  The  student  is  referred  to  Maver's  American  Telegraphy,  pages  494-508  and  to 
Railway  Signaling  published  by  The  Electric  Journal  of  Pittsburgh,  Pa.  This  is  a 
reprint  of  a  series  of  articles  which  appeared  in  The  Electric  Journal  during  1907 
and  it  gives  a  great  deal  of  information  on  the  subject.  The  Union  Switch  and 
Signal  Company  of  Swiss  vale,  Pa.,  and  The  Hall  Signal  Company  of  Elizabeth, 
N.  J.,  will  send  descriptive  circulars  to  engineering  students  who  are  interested  in 
railway  signaling. 


256  ELECTRIC   LIGHTING. 

Electric  Railroads: 

W.  C.  Gotshall,  Electric  Railway  Economics,  McGraw-Hill  Book  Co.,  1903. 

Ashe  &  Keily,  Electric  Railways,  Van  Nostrand,  1905. 

Wilson  &  Lydall,  Electrical  Traction,  Longmans,  Green  &  Co.,  1907. 

Herrick  &  Boynton,  American  Electrical  Railway  Practice,  McGraw-Hill  Book 

Co.,  1907. 
Sheldon   &   Hausman,   Electric   Traction   and   Transmission   Engineering,   Van 

Nostrand,  1911. 

C.  F.  Harding,  Electric  Railway  Engineering,  McGraw-Hill  Book  Co.,  1911. 
Section  13  of  The  Standard  Handbook  for  Electrical  Engineers  on  Traction,  by 
A.  H.  Armstrong,  McGraw-Hill  Book  Co. 


* 

APPENDIX  A. 

DIELECTRIC    STRESSES. 

The  equation  of  the  condenser  is 


Q  =  CE  (I) 

in  which  E  is  the  electromotive  force  in  volts  applied  to  the 
condenser  plates,  Q  is  the  amount  of  charge  in  coulombs  drawn 
out  of  one  plate  and  forced  into  the  other  plate,  and  C  is  the 
capacity  of  the  condenser  in  farads.* 

The  capacity  in  farads  of  a  parallel  plate  condenser  with  air  as 
the  dielectric  is 

C=  884  Xio-16^  (2) 

Bv 

in  which  a  is  the  area  of  one  of  the  plates  (sectional  area  of  the 
dielectric)  in  square  centimeters,  and  x  is  the  thickness  of  the 
dielectric  in  centimeters. 

To  substitute  oil  or  any  other  dielectric  for  the  air  increases 
the  capacity  of  a  condenser  in  a  certain  ratio  k  so  that  the 
capacity  may  then  be  expressed  by  the  equation 

=  884  X  io-16^.  (3) 

•v 

The  factor  k  is  called  the  inductivity  of  the  dielectric  (also  some- 
times called  specific  capacity  of  the  dielectric).  Thus  the  induc- 
tivity of  kerosene  is  about  2,  which  means  that  the  capacity  of 
an  air  condenser  is  doubled  if  kerosene  is  substituted  for  the 
air  dielectric. 

In  the  following  discussion  the  letter  B  is  used  to  designate 
the  factor  884  X  io~16. 

*  An  elementary  discussion  of  the  condenser  is  given  on  pages  162-173  of  Frank- 
lin and  MacNutt's  Elements  of  Electricity  and  Magnetism,  The  Macmillan  Co.,  1908. 
18  257 


258  ELECTRIC    LIGHTING. 

Gauss's  theorem. — A  theorem  of  fundamental  importance  in 
electrostatic  theory  is  as  follows:  The  total  electric  flux  $  ema- 
nating from  a  charged  body  is  equal  to  Q  -f-  B,  or  the  total  charge 
on  a  body  is  equal  to  B$,  where  Q  is  the  charge  in  coulombs 
and  $  is  electric  flux  expressed  in  volt-centimeters  in  air.  (An 
electric  field  intensity  is  expressed  in  volts  per  centimeter,  and 
the  product  of  this  field  intensity  by  an  area  in  square  centimeters 
gives  electric  flux  in  volt-centimeters,  the  area  being  perpendicular 
to  the  field.) 

When  applied  to  a  parallel-plate  air  condenser,  Gauss's 
theorem  may  be  derived  by  multiplying  both  members  of  equa- 
tion (2)  by  E  (the  electromotive  force  between  the  plates), 

giving 

T? 
CE   =    Qcoulombt   =    Bd 1 

but  E  -f-  x  is  the  electric  field  intensity  between  the  plates  in 
volts  per  centimeter,  so  that  a  X  E  •£•  x  is  the  electric  flux  from 
plate  to  plate  in  volt-centimeters  and  therefore,  a  X  E  -f-  x  =  $ 
whence  we  have 

Q  =  Bj.  (4) 

Gauss's  theorem  may  be  derived  for  a  parallel  plate  condenser 
with  any  dielectric  by  multiplying  both  members  of  equation 
(3)  by  E  (the  electromotive  force  between  the  plates),  giving 

-p> 

CE  =  Q  =  B  .a.k-, 
x 

but  E  -f-  x  is,  as  before,  the  electric  field  intensity  between  the 
plates  and  k  X  E  -r-  x  may  be  defined  as  the  electric  flux  density* 
in  the  dielectric,  so  that  a  X  kE  -r-  x  is  the  total  flux,  and  we 
thus  arrive  again  at  equation  (4). 

*  The  product  kf  which  is  here  called  electrical  flux  density  or  electrical  strain, 
was  called  dielectric  polarization  by  Maxwell.  See  Maxwell's  Treatise. 


DIELECTRIC    STRESSES. 


259 


MAGNETIC  AND  ELECTRIC  PARALLEL. 
c8  =  n&C,  F  =  kf, 

is   intensity    of  magnetic       where    /    is  intensity  of  electric  field 

in  volts  per  centimeter  (E-s-x),  k 
is  the  inductivity  of  the  medium, 
and  F  is  the  electric  flux  density 
in  volt-centimeters  per  square  cen- 
timeter. 


where 

field  in  gausses,  /n  is  the  perme- 
ability of  the  medium,  and  oB  is  the 
magnetic  flux  density. 


ELECTRICAL  STRESS  AND  MECHANICAL  STRESS. 

The  intensity  of  an  electric  field  in 
volts  per  centimeter  (or  the  volts 
per  centimeter  in  a  layer  of  dielectric 
between  metal  plates)  is  frequently 
called  electrical  stress,  and  the  electric 
flux  density  kf  in  the  dielectric  is 
frequently  called  the  electrical  strain. 
Therefore  we  have 


The  stretching  force  per  unit  of  sec- 
tional area  of  a  rod  is  called  the 
stress  on  the  rod,  and  the  elonga- 
tion of  unit  length  of  the  rod  is 
called  the  strain;  and  the  strain  is 
proportional  to  the  stress.  That  is 


(  mechanical 
I      strain 


nical)  f  mechanical)  ( 

in     J=WXt      stress      /'  I 


electrical )  _  ,        (  electrical ) 
strain    )  \     stress     f* 


where    n    is  a  constant  for  a  given 
substance. 

The  potential  energy  of  mechanical 
strain  per  cubic  centimeter  of  the 
strained  substance  is  equal  to  one- 
half  the  product  of  stress  and  strain. 


The   elastic  condition   of   a  substance 

can  be  specified  as  follows: 
(a)  By  giving  the  stress  in  pounds  per 

square  inch; 
(&)  By     giving     the    strain,     as     for 

example  the  percentage  elongation  of 

a  wire  under  tension;  or 
(c)  By  giving  the  potential  energy  per 

unit  volume  of  the  strained  substance. 


where     k    is  a  constant  for  a  given 
dielectric. 

The  potential  energy  of  electrical  strain 
per  cubic  centimeter  of  the  dielectric 
is  equal  to  one-half  the  product  of 
electrical  stress  (/)  and  electrical 
strain  (kf). 

The   electric   condition   of   a   dielectric 

can  be  specified  as  follows: 
(a)  By   giving    the    electrical  stress  in 

volts  per  centimeter; 
(&)   By    giving    the    electrical  strain  in 

volt-centimeters  or  in  coulombs  per 

square  centimeter*;  or 
(c)  By  giving  the  potential  energy  per 

unit  volume  of  the  dielectric. 


*  Electric  flux  can  be  expressed  in  coulombs  according  to  equations  (2)  and  (3) 
and  therefore  electric  flux  density  can  be  expressed  in  coulombs  per  square  centi- 
meter. If  a  metal  ball  has  Q  coulombs  of  charge  per  square  centimeter  of  its 
surface,  then  Q/B  volt-centimeters  of  electric  flux  emanate,  from  each  square  centi- 
meter of  the  ball,  according  to  equation  (4),  or,  in  other  words,  the  electric  flux 
density  in  the  dielectric  near  the  surface  of  the  ball  (  =  kf)  is  Q/B  volt-centimeters 
per  square  centimeter,  and  therefore  the  electric  field  intensity  near  the  surface 
of  the  ball  is  Q/B  -f-  k  volts  per  centimeter. 


260  ELECTRIC    LIGHTING. 

Electric  stresses  in  plane  layers  of  different  dielectrics. — 

Consider  two  metal  plates  with  air  and  glass  between  them  as 
shown  in  Fig.  I.  The  thing  which  is  constant  throughout  the 
region  between  the  metal  plates,  that  is,  the  thing  which  has  the 
same  value  in  glass  and  air  is  the  electric  flux  density  kf,  because 
there  are  equal  and  opposite  charges  on  two  plates,  and,  therefore, 
according  to  Gauss's  theorem  the  total  flux  passing  out  from  the 
positively  charged  plate  (+  (?)  is  equal  to  the  total  flux  passing 
in  towards  the  negatively  charged  plate  ( —  Q) .  Now  since  kf 
is  the  same  in  the  glass  and  in  the  air,  and  since  k  =  I  for  air 
and  k  =  6  for  glass,  therefore,  the  electric  field  intensity  or  stress 
in  volts  per  centimeter  (/)  is  six  times  as  great  in  the  air  as  in  the 
glass. 

Consider  the  special  case  in  which  the  glass  and  air  are  of 
equal  thickness  as  indicated  in  Fig.  I.  Then  six  sevenths  of  the 
battery  voltage  is  impressed  on  the  air  layer  and  one  seventh  on 
the  glass  layer.  If  glass  and  air  are  each  I  centimeter  thick,  and 
if  the  total  voltage  is  35,000  volts,  then,  assuming  the  air  not  to 
break  down,  the  voltage  across  the  air  will  be  30,000  volts, 
and  the  voltage  across  the  glass  will  be  5,000  volts. 

If  the  glass  plate  is  removed,  leaving  2  centimeters  of  air, 
then  the  electrical  stress  on  the  air  will  be  17,500  volts  per  centi- 
meter. Therefore  the  electrical  stress  in  the  air  between  two 
plates  2  centimeters  apart  is  increased  from  17,500  volts  per 
centimeter  to  30,000  volts  per  centimeter  by  filling  half  of  the 
space  between  the  plates  with  glass  of  inductivity  6. 

This  effect  can  be  shown  in  a  very  beautiful  manner  by  con- 
necting two  metal  plates  to  a  high-voltage  transformer  and  ad- 
justing the  plates  to  a  distance  such  that  the  intervening  air 
layer  is  barely  sufficient  to  sustain  the  voltage.  Then  if  a  glass 
plate  be  introduced  between  the  metal  plates,  the  electrical  stress 
in  the  remaining  air  will  be  increased  sufficiently  to  break  the 
air  down  at  each  reversal  of  the  alternating  voltage,  as  shown  by 
the  bluish  luminosity  of  the  air  layer. 

The  above  discussion  of  the  stresses  in  layers  of  glass  and 


DIELECTRIC   STRESSES. 


261 


air  as  based  on  Fig.  I  can  be  simplified  as  follows:  Imagine  a 
thin  sheet  of  metal  mm  to  be  placed  between  the  air  and  glass 
as  shown  in  Fig.  2.  We  thus  have  two  exactly  similar  conden- 
sers, C'  and  C,  of  glass  and  air,  and  the  capacity  of  the  glass 


— I'l'l'lil'l'l'l'l 


Fig.  1. 


Fig.  2. 


condenser  is  six  times  as  great  as  the  capacity  of  the  air  con- 
denser, according  to  equations  (2)  and  (3).  But  the  charges 
on  C'  and  C  are  the  same  because  they  have  been  charged  in 
series.  Therefore  the  voltage  across  the  glass  condenser  is  one- 
sixth  of  the  voltage  across  the  air  condenser,  according  to  equa- 
tion (i). 

The  concentration  of  the  greater  part  of  the  voltage  upon 
the  air  layer  in  Figs.  I  and  2  is  exactly  analogous  to  the  con- 
centration of  the  greater  part  of  the  magnetomotive  force  of  a 
dynamo  field-winding  upon  the  air  gap  in  the  magnetic  circuit; 
only  a  small  portion  of  the  magnetomotive  force  is  required  to 
force  the  magnetic  flux  through  the  highly  permeable  iron,  and 
a  large  portion  of  the  magnetomotive  force  is  required  to  force 
the  magnetic  flux  through  the  less  permeable  air  layer.  A  small 
portion  of  the  battery  voltage  is  required  to  force  the  electric 
flux  through  the  highly  inductive  glass  in  Fig.  I  and  a  large 
portion  of  the  voltage  is  required  to  force  the  electric  flux  through 
the  less  inductive  air. 

Mechanical  analog  of  Fig.  1. — A  difficulty  in  obtaining  a  simple 
mechanical  idea  of  the  concentration  of  the  greater  part  of  the 


262 


ELECTRIC   LIGHTING. 


battery  voltage  on  the  air  layer  in  Fig.  I  arises  from  the  following 
fact :  the  glass  and  the  air  are  in  series  in  Fig.  I  (and  the  electric 
flux  density  or  electric  strain  or  yield,  in  the  two  is  the  same), 
whereas  two  mechanical  elements  have  the  same  stress  when  they 
are  in  series;  to  have  the  same  strain  or  yield,  two  mechanical 
elements  must  be  in  parallel.  Thus  Fig.  3  shows  a  column  of 
steel  and  a  column  of  rubber  equally  compressed  between  two 
bars  A  and  B  (the  steel  and  rubber  columns  are  in  parallel 


Fig.  3. 


Fig.  4. 


and  they  are  equally  shortened) ;  but  the  easily  yielding  rubber 
(high  inductivity)  supports  a  small  part  of  the  compressing 
force,  and  the  stiff  steel  (low  inductivity)  supports  a  large  part  of 
the  compressing  force. 

Distribution  of  electrical  stress  in  the  region  between  core 
and  sheath  of  an  insulated  cable,  core  and  sheath  being  cylin- 
drical and  coaxial. — Consider  unit  length  of  the  wire  core  of  a 
cable  and  let  Q  be  the  amount  of  electric  charge  thereon.  Let  / 
be  the  electric  field  intensity  in  volts  per  centimeter  at  the  point 
p  in  the  insulation  distant  r  from  the  axis  of  the  cable  and  let  k 
be  the  inductivity  of  the  insulating  material  at  p.  Then  kf 
(see  Fig.  4)  is  the  electric  flux  density  at  p,  and  2wr  X  kf  is  the 
flux  across  the  cylindrical  surface  cc  (of  unit  length),  that  is 
2wrkf  is  the  flux  emanating  from  Q,  and,  therefore,  according 
to  equation  (4),  we  have 


DIELECTRIC   STRESSES.  263 

Q  =  B  X  2irrkf 


or 


In  interpreting  this  equation  we  will  consider  two  cases, 
namely,  (a)  The  case  in  which  the  cable  insulation  is  all  of  one 
kind  of  material,  and  (b)  The  case  in  which  the  cable  insulation  is 
built  around  the  core  in  layers  of  decreasing  inductivity. 

In  the  first  case  r  is  the  only  variable  in  equation  (5)  and  the 
electrical  stress  at  any  point  in  the  cable  insulation  is  inversely 
proportional  to  the  distance  r  from  the  axis  of  the  cable.  The 
electrical  stress  is  greatest  near  the  wire  core  and  least  near  the 
sheath.  This  concentration  of  the  stress  near  the  wire  core  of  a 
cable  makes  it  impossible  to  utilize  the  full  electrical  strength  of 
a  cable  insulation  in  case  (a).  In  a  somewhat  similar  manner  the 
mechanical  stress  in  the  steel  of  a  gun  barrel  is  concentrated  near 
the  bore  and  consequently  it  is  impossible  to  utilize  the  full 
mechanical  strength  of  a  solid  forged  gun  barrel.  The  concentra- 
tion of  stress  near  the  bore  will  start  cracks  in  the  walls  while 
the  outer  portions  of  the  gun  barrel  are  very  far  indeed  from 
being  severely  strained. 

In  the  second  case  if  we  could  select  the  materials  for  the  suc- 
cessive layers  of  cable  insulation  so  as  to  decrease  k  as  r  increases 
it  would  be  possible  to  keep  the  product  kr  constant  and  then  the 
electrical  stress  /  in  volts  per  centimeter  would  be  the  same  in 
value  throughout  the  insulating  material.  It  is  impracticable 
to  accomplish  this  result  completely,  but  high-voltage  cable 
insulation  is  usually  put  on  in  two  or  three  layers  decreasing  in 
inductivity  outwards.  Such  a  cable  is  said  to  have  a  graded 
insulation. 

There  is  an  interesting  mechanical  analogy  to  the  graded  cable 
insulation.  If  a  thick-walled  steel  tube  is  subjected  to  internal 
pressure  as  in  a  cannon,  the  material  next  the  bore  is  stretched 
to  its  stress-limit  before  the  outer  portions  of  the  steel  are  brought 
into  full  action.  If  easily  yielding  (highly  elastic  like  rubber)  steel 


264 


ELECTRIC   LIGHTING. 


could  be  used  for  the  inner  portions  of  the  gun  tube,  then  the 
greater  yield  of  the  inner  material  would  tend  to  bring  all  of 
the  material  of  the  tube  up  to  the  limiting  stress  simultaneously.* 
There  is  in  fact  but  little  variation  in  the  elastic  coefficient  of 
various  kinds  of  steel,  and  this  method  of  gun  construction  is 
therefore  impracticable.  There  are,  however,  great  differences 
in  the  inductivities  of  different  insulating  materials,  and  therefore 
the  grading  of  cable  insulation  is  to  some  extent  practicable. 

Observable  effects  dependent  upon  variations  of  dielectric 
inductivity. — The  greatest  obstacle  to  a  clear  understanding  of 
the  theory  of  dielectric  stress  is  that  students  and  engineers  are 
not  familiar  with  the  simple  observable  effects  which  involve 
inductivity.  Indeed  some  of  these  effects  are  so  simple  that  it- 
is  sufficient  merely  to  describe  them  as  follows: 


Fig.  5. 


Fig.  6. 


The  lines  of  force  in  an  electric  field  converge  upon  and  pass 
through  a  glass  rod  (high  inductivity),  and  the  lines  of  force 
in  a  magnetic  field  converge  upon  and  pass  through  an  iron  rod 
(high  permeability).  A  glass  rod  suspended  in  an  electric  field 
oscillates  to  and  fro  through  an  equilibrium  position  parallel 
to  the  field  in  the  same  way  that  a  suspended  iron  rod  oscillates 
in  a  magnetic  field.  (Figs.  5  and  6.) 

A  glass  plate  is  drawn  into  the  intense  electric  field  between 
positively  charged  metal  plates  in  the  same  way  that  a  piece  of 
iron  is  drawn  into  the  intense  magnetic  field  between  two  opposite 
magnet  poles  as  shown  in  Figs.  7  and  8.  In  the  same  way  oil 

*  The  steel  tube  of  a  cannon  is  strengthened  in  practice  by  shrinking  a  series  of 
jackets  over  the  tube. 


DIELECTRIC    STRESSES. 


265 


and  especially  water  is  drawn  into  the  most  intense  part  of  an 
electric  field. 

A  thin  glass  cell  partly  filled  with  oil  and  provided  with 
metal  terminals  A  and  B  is  placed  in  a  lantern  and  the  terminals 
A  and  B  are  connected  to  a  Toepler-Holtz  machine,  as  indicated 


glass  plate 


iron  plate 


j 

^ 

H^ 

x^ 

I  "/ 

N 

4— 

4- 

s          z 

)                 / 

\  

/ 

=±= 

\ 

,,,,,..,,~,-\ 

~___        _, 

f/t  Tt,  ,,,,,  ,,,,\ 

Fig.  7. 


Fig.  8. 


in  Fig.  9.  The  oil  (high  inductivity)  is  drawn  up  as  shown,  and 
eventually  a  column  of  oil  is  formed  reaching  up  to  terminal  A. 
In  the  same  way  a  magnetic  liquid  (permeability  greater  than 

unity)  would  be  drawn  up  to  a  

magnet  pole.    Bubbles  of  air  ris-     _j 
ing  in  oil  in  front  of  a  pointed 
metal  terminal  (charged)  are  re- 
pelled. 

A  charged  gold-leaf  electro- 
scope is  placed  in  a  lantern  with 
the  plate  of  the  electroscope  con- 
nected by  a  fine  wire  to  an  in- 
sulated plate  PP  on  the  lec- 
ture table,  as  shown  in  Fig.  10.  When  a  slab  of  paraffin 
W  is  placed  in  the  region  CC,  the  electroscope  leaves  fall 
slightly.  The  capacity  of  the  condenser  CC  has  been  in- 
creased by  the  paraffin  slab  and  a  greater  portion  of  the  charge 
on  the  insulated  system  flows  into  PP  thus  decreasing  the 


Fig.  9. 


266  ELECTRIC    LIGHTING. 

charge  on  the  electroscope  leaves.  If  one  had  two  inflated 
rubber  bags  connected  by  a  tube,  and  if  one  were  to  make  the 
walls  of  one  bag  more  yielding  by  dissolving  off  a  portion  of 
the  rubber  (if  that  were  possible) ,  then  the  weakened  bag  would 
swell  and  the  other  bag  would  shrink.  The  plate  of  paraffin 
makes  the  dielectric  around  PP  more  yielding  and  some 
charge  flows  from  EE  into  PP. 


Dielectric  hysteresis. — The  most  prominent  kind  of  dielectric 
hysteresis  is  a  kind  which  is  closely  analogous  to  what  is  tech- 
nically called  elastic  lag  in  mechanics.  Glass,  for  example,  when 
subjected  to  a  mechanical  stress  takes  on  a  certain  amount  of 
strain  (deformation)  quickly,  after  which  the  strain  slowly  in- 
creases for  a  time;  and  when  the  stress  is  removed,  a  remnant  of 
the  strain  persists  for  a  time.  This  kind  of  hysteresis  is  some- 
times called  viscous  hysteresis,  and  it  is  very  different  from  the 
magnetic  hysteresis  in  iron  or  steel,  although  a  slight  amount  of 
viscous  hysteresis  does  exist  in  very  soft  iron. 

Dielectric  hysteresis  of  the  viscous  type  has  long  been  known 
to  exist,  and  it  is  the  cause  of  the  so-called  "residual  charge" 
which  accumulates  in  a  Leyden  jar  when  the  jar  is  highly  charged 
and  then  completely  discharged  and  allowed  to  stand. 

A  Leyden  jar  is  charged.     The  coat-       A     rubber     tube     is     stretched.     This 
ings   of    the    jar    are    then    momen-  stretch     corresponds     to     the     elec- 

tarily  connected  by  wire,  and  then  trical  strain  of  the  glass  walls  of  the 

the    jar    is    left    standing    on    open          Leyden   jar.     The  end   of   the   tube 
circuit.     After  a  time   the  coatings  is    momentarily    released,    and    the 

are   again   connected   and   a   second  end    is    then    clamped    fast    in   what 

slight  discharge  is  obtained.  seems    to    be    its    equilibrium    posi- 

tion. After  a  time  the  end  is  again 
released  and  a  second  slight  "dis- 
charge" or  movement  takes  place. 


DIELECTRIC    STRESSES. 


267 


Dielectric  strength. — The  voltage  required  to  puncture  a  layer 
of  dielectric  between  flat  metal  plates  is  approximately  propor- 
tional to  the  thickness  of  the  dielectric  layer.  That  is  to  say,  a 
definite  electrical  stress  in  volts  per  centimeter  is  required  to 
break  down  a  dielectric,  and  this  limiting  electrical  stress  meas- 
ures what  is  called  the  dielectric  strength. 

TABLE   OF   DIELECTRIC   STRENGTHS.* 


Substance. 

Strength  in 
Volts  per  Inch. 

Substance. 

Strength  in 
Volts  per  Inch. 

Oil  of  turpentine  

235,000 

Beeswaxed  paper  

1,350,000 

217  ^OO 

Air  (thickness  5  cm  ) 

CQ  CQO 

Olive  oil  

2O5,OOO 

CO2  (thickness  5  cm.)  .... 

56,750 

Paraffine  (melted)  

I4O,OOO 

O  (thickness  5  cm.)  

55,500 

Kerosene  oil  

I25,OOO 

H  (thickness  5  cm.)  

37,750 

Paraffine  (solid)  

•*2c,,ooo 

Coal  gas  (thickness  5  cm.) 

55,750 

Paraffined  paper  

900,000 

Concentration  of  electrical  stresses  by  points. — The  ease  with 
which  a  bar  of  hard  tool-steel  can  be  broken  when  a  sharp-bot- 
tomed nick  is  made  in  one  side  of  the  bar  is  well  known.  Fig.  1 1 
shows  the  lines  of  stress  pass- 
ing around  the  bottom  of  a 
sharp  groove  in  a  bent  bar. 
The  stress  is  very  greatly  con- 
centrated near  the  bottom  of 
the  groove,  and  the  groove 
deepens  by  the  formation  of  a 
crack.  The  stress  is  then  con- 
centrated at  the  edge  of  the  crack,  and  the  crack  is  extended 
farther  and  farther  until  the  bar  is  broken  in  two. 

It  is  perhaps  not  generally  known  that  the  glass-cutting 
diamond  does  not  make  a  scratch.  Such  a  scratch  would  be  a 
shallow  flat-bottomed  groove,  and  no  very  great  concentra- 
tion of  stress  would  occur  at  the  bottom  of  such  a  groove  when 
the  pane  of  glass  is  slightly  bent.  The  end  of  a  cutting  diamond 

*From  the  measurements  of  Macfarlane  and  Pierce,  Physical  Review,  Vol.  I, 
page  165,  1894. 


Fig.  11. 


268 


ELECTRIC    LIGHTING. 


is  a  perfectly  rounded  "corner"  of  a  natural  diamond  crystal 
(the  diamond  is  a  crystal  with  curved  faces) ,  and  when  a  cutting 
diamond  is  drawn  properly  across  a  pane  of  glass  a  minute  crack 
is  formed  under  the  diamond  on  account  of  the  excessive  local 
compression.  This  crack  causes  a  very  great  concentration  of 
stress  when  the  pane  of  glass  is  subjected  to  a  very  slight  bending 
action,  and  the  result  is  that  the  crack  runs  through  the  pane. 


Fig.  12. 

When  a  diamond  is  drawn  heavily  across  a  pane  of  glass  a  very 
considerable  exertion  is  required  to  break  the  glass  and  the  crack 
does  not  always  follow  the  groove.  When  a  diamond  is  drawn 
properly  across  a  pane  of  glass  a  very  slight  bending  effort  is 
sufficient  to  break  the  glass,  and  the  break  nearly  always  follows 
the  minute  crack  produced  by  the  diamond. 

A  very  interesting  accident  occurred  at  the  Bethlehem  Steel 
Works  a  number  of  years  ago  when  an  attempt  was  made  to 
strengthen  a  crank-disk  by  shrinking  a  collar  upon  it.  The  disk 
had  a  crank-pin  on  one  side,  and  the  disk  sheared  off  along  the 
dotted  line  ap  in  Fig.  12  on  account  of  the  excessive  concentra- 
tion of  stress  at  the  reentrant  angle  a.  The  fine  curved  lines 
show  the  approximate  trend  of  the  stress  lines  in  the  disk  due 
to  the  collar  CC. 


DIELECTRIC   STRESSES. 


269 


W 


p 

p 

Fig.  13. 


An  interesting  experiment  is  to  place  a  small  piece  of  window 
glass  on  a  flat  plate  of  steel  (or  plate  glass)  and  press  a  sharp- 
pointed  file  against  it  as  shown  in  Fig.  13. 
The  stresses  in  the  window  glass  are  very 
greatly  concentrated  at  the  sharp  point  of  the 
file,  and  it  takes  but  little  force  on  the  file 
to  break  the  glass  to  pieces.  If,  however,  a 
bit  of  soft  copper  is  placed  under  the  point 
of  the  file,  one  cannot  push  hard  enough  to 
break  the  glass;  the  copper  yields  (breaks  down  mechanically) 
and  distributes  the  stress. 

When  a  voltage  is  applied  to  the  metal  terminals  MM  in 
Fig.  14,  the  electric  lines  of  force  (the  electrical  stress  lines) 
converge  upon  the  sharp  metal  point,  and  the  electrical  stress 
is  very  greatly  concentrated  near  the  point.  Indeed  a  compara- 
tively low  voltage  will  rupture  the  glass  plate  in  Fig.  14  because 
of  the  starting  of  an  electric  rupture  by  the  excessive  concentra- 
tion of  the  stress  near  the  metal  point.  To  produce  this  result, 
however,  the  region  rr  must  be  filled  with  a  substance  of  great 


electric 
lines  of  force 


Fig.  14. 


Fig.  15. 


dielectric  strength  like  turpentine  or  wax.  If  the  region  rr 
is  filled  with  a  substance  of  low  dielectric  strength  like  air,  the 
portion  in  the  immediate  neighborhood  of  the  metal  point  breaks 
down  electrically  and  becomes  a  conductor,  and  the  resultant 
distribution  of  electrical  stress  in  the  glass  plate  (which  is  shown 


270 


ELECTRIC   LIGHTING. 


in  Fig.  15)  is  the  same  as  if  the  glass  plate  were  between  two 
flat  metal  plates  as  shown  in  Fig.  16.  Under  these  conditions 
the  electrical  stress  in  the  glass  is  nearly  uniform,  and  a  very 

high  voltage  is  required  to  puncture 
the  glass  plate,  because  there  is  no  re- 
gion of  concentrated  stress  to  start 
the  electrical  break-  down. 

Having  air  around  the  metal  point 
in  Fig.  14  is  like  having  a  bed  of  soft 
copper  around  the  point  of  the  file  in 
Fig.  13.  The  copper  breaks  down 
mechanically  and  distributes  the 
stress,  thus  preventing  excessive  con- 
centration of  stress  near  the  point  of 
the  file  and  the  starting  of  a  crack  thereby.  The  air  breaks 
down  electrically  and  distribute!  the  stress,  thus  preventing  ex- 
cessive concentration  of  stress  near  the  metal  point  and  the 
starting  of  an  electric  puncture  thereby. 

An  electrical  breakdown  in  a  solid  dielectric  (and  usually  in 
liquid  and  gaseous  dielectrics  also)  is  always  in  the  form  of  a 
puncture,  that  is  the  breakdown  occurs  along  a  line;  and  this 
line  of  breakdown  is  an  electrical  conductor.  Therefore  the  elec- 
trical stresses  in  the  dielectric  are  concentrated  at  the  end  of  an 
incipient  puncture,  as  at  a  metal  point,  and  the  puncture  is  thus 


Fig.  16. 


Fig.  17. 

carried  through  the  dielectric  or  into  regions  where  the  electrical 
stresses  were  far  below  the  breakdown  value  before  the  puncture 
started.  Thus  Fig.  17  shows  the  electric  lines  of  force  between 


DIELECTRIC    STRESSES. 


271 


two  metal  balls,  and  Fig.  18  shows  how  the  electric  lines  of  force 
rearrange  themselves  when  an  electric  puncture  starts. 


Fig.  18. 

Maximum  stress  in  homogeneous  cable  insulation  for  given 
voltage  between  core  and  sheath. — Equation  (5)  cannot  be  used 
to  calculate  the  actual  value  of  the  electrical  stress  /  at  a  given 
distance  r  from  the  axis  of  the  cable  because  the  value  of  Q  is 
not  known.  The  quantity  which  is  always  specified  or  which 
can  be  most  easily  observed  is  the  voltage  E  between  the  core 
and  the  sheath,  and,  therefore,  it  is  desirable  to  derive  an  equation 
which  gives  /  in  terms  of  E  as  follows: — Let  RI  be  the  radius 
of  the  wire  core  and  let  Rz  be  the  inside  radius  of  the  sheath, 
both  expressed  in  centimeters.  It  is  required  to  find  the  total 
voltage  along  the  line  ab,  Fig.  19.  Consider  the  element  Ar  of  the 


wire 


Fig.  19. 


line  ab.  The  voltage  along  this  element  is  /-Ar  because/  is  the 
volts  per  centimeter  at  Ar  (compare  Fig.  4).  Therefore  we  have 
AE  =  /-Ar,  or  using  the  value  of  /  from  equation  (5)  we  have 


272  ELECTRIC    LIGHTING. 

Q        Ar 


whence  by  integrating*  between  the  limits  r  =  R\  to  r  =  Rz  we 
have 


Therefore  the  entire  factor    Q/27rBk    inequation  (5)  is  equal  to 
E/[\oge(Rz!Ri)],    and  equation  (5)  may  be  written: 

(7) 


1          Kz\     r 

loge  I   «•   I 

\.Ki/ 

or,  reducing  to  common  logarithms,  we  have 

0435 -E        i 


log 


(t) ' 


The  greatest  value  of  /  occurs  at  the  surface  of  the  wire  core 
where   r  =  R\   and  therefore  from  equation  (8)  we  have 

0.435  E  X      v 


/max    ~~ 


in  which  /max  is  expressed  in  volts  per  centimeter  if  E  is  ex- 
pressed in  volts  and  RI  and  RZ  in  centimeters,  or  in  volts  per 
inch  if  E  is  expressed  in  volts  and  RI  and  RZ  in  inches.  For 
example  consider  a  cable  having  a  quarter-inch  wire  core  (Ri  = 
0.125  inch)  and  one  half-inch  of  insulation  (R%  =  0.625  inch)  with 
10,000  volts  between  wire  and  sheath.  Then  the  maximum 
electrical  stress  is  49,700  volts  per  inch  and  the  electrical  stress 
near  the  sheath  is  9,940  volts  per  inch.  On  the  other  hand, 
half  an  inch  of  insulation  between  flat  metal  plates  would  be  under 
a  uniform  stress  of  20,000  volts  per  inch  with  10,000  volts  be- 
tween the  plates. 

*  Of  course  k  is  assumed  to  be  constant;  that  is  the  cable  insulation  is  all  one 
kind  of  material. 


DIELECTRIC   STRESSES.  273 

Maximum  electrical  stress  between  parallel  wires. — Figure  20 
is  a  sectional  view  of  the  two  wires  W  and  W"  and  it  is  desired 
to  find  the  expression  for  the  electrical  stress  /  at  any  point  p 
distant  x  centimeters  from  the  axis  of  W  when  there  is  +  Q 
coulombs  of  electric  charge  on  each  centimeter  of  W  and  —  Q 
coulombs  on  each  centimeter  of  W".  The  wires  are  small  in 
diameter  as  compared  with  their  distance  apart  D,  and  therefore 


A-^7^^ 


Fig.  20. 

the  charge  may  be  assumed  to  be  uniformly  distributed  around 
each  wire,  and  the  electric  field  due  to  either  wire  alone  may  therefore 
be  assumed  to  radiate  symmetrically  around  the  wire  exactly  as 
if  the  wire  were  surrounded  by  a  co-axial  sheath. 

Let  /'  be  the  electrical  stress  at  p  due  to  W  and  let  /" 
be  the  electrical  stress  at  p  due  to  W".  Then  according  tc 
equation  (5)  we  have: 

f  =     Q    • L  G) 

2irBk    x 
and 

1"   =  2wBk  '  (D  -  xY  , 

But  the  total  electrical  stress  at  p  is  /'  +  /"  and  therefore  we 
have 


and  the  voltage    AE    along  the  element    A*    is  equal  to   /-A* 
so  that 


_          \x,  (iii) 

19 


274  ELECTRIC   LIGHTING. 

whence,  by  integrating*  between  the  limits    x  =  R    and    x  = 
D  —  R   (from  surface  to  surface  of  the  wires  in  Fig.  20)  we  have: 

E  =  — —  •  loe 


where  R  is  the  radius  of  each  wire  and  D  '  is  the  distance  between 
centers  of  wires. 

From  equation  (iv)  we  find  the  value  of  the  factor    Q/(2wBk) 
to  be    E/{2  loge  [(D  —  R)!R]}    so  that  equation  (10)  becomes 


(V) 


The  maximum  value  of  /  occurs  at  the  surface  of  either  wire 
where  x  =  R  (or  where  x  =  D  —  R).  Furthermore  i/R  is 
quite  large  as  compared  with  i/(D  —  R).  Therefore  substitut- 
ing R  for  x  in  equation  (v)  and  discarding  i/(D  —  R)  as 
negligible  in  comparison  with  i/R,  we  have 


R 

whence,  using  ordinary  logarithms  we  have 

0435  E 


/m»*    -  /  r>  7P\  '  (jj) 


For  most  practical  purposes    D  —  R    is  sensibly  equal  to    D 
and  therefore  equation  (n)  may  be  written: 

-  0-435  £ 

/max  - 


2  R  log  i   R 

in  which   /max    is  expressed  in  volts  per  centimeter  if    E    is  ex- 
pressed in  volts  and    D    and    R    in  centimeters,  or  in  volts  per 

*  Of  course   k   is  assumed  to  be  constant;  that  is  the  wires  are  surrounded  by 
insulating  material  all  of  one  kind. 


DIELECTRIC   STRESSES. 


275 


inch  if  E  is  expressed  in  volts  and  D  and  R  in  inches.  For 
example  consider  a  transmission  line  consisting  of  two  quarter- 
inch  wires  (R  =  0.125  inch)  24  inches  apart  center  to  center 
(D  =  24  inches)  with  50,000  volts  between  the  wires.  Then 
the  maximum  electrical  stress  is  38,100  volts  per  inch. 

The  equalization  of  the  electrical  stresses  in  the  insulation  of 
transformer  terminals. — A  certain  amount  of  electric  flux  starts 
out  from  the  wire  core  of  a  cable,  and  this  same  amount  of  flux 
continues  outwards  unchanged  in  value,  and  therefore  the  flux 
density  decreases  at  increasing  distances  from  the  core.  In  the 
case  of  a  long  cable,  the  electrical  stress  in  the  insulation  can  be 


end  view 


side  view 


Fig.  21. 


made  uniform  by  the  grading  of  the  inductivity  of  the  insulation 
as  above  explained.  In  the  case  of  a  short  rod,  the  electric  flux 
which  emanates  from  the  rod  can  be  more  and  more  crowded 
together  endwise  at  increasing  distances  from  the  rod  so  as  to 
compensate  for  the  circumferential  spreading  and  thereby  give  the 
same  electric  flux  density  and  the  same  electrical  stress  throughout 
the  insulation.  This  crowding  together  endwise  of  the  electric 
flux  is  accomplished  by  dividing  the  insulation  into  layers  of  equal 
thickness  which  are  separated  by  sheets  of  tin-foil  as  shown  in 


276 


ELECTRIC    LIGHTING. 


Fig  21.  This  arrangement  of  the  insulation  of  a  rod  is  called 
the  condenser  type  of  insulation. 

The  principle  of  the  condenser  type  of  insulation  may  be 
understood  with  the  help  of  Fig.  22,  which  shows  two  condensers 

c  and  C  connected  in  series  to  a 
battery.  The  two  condensers  receive 
the  same  amount  of  charge  Q  when 
arranged  in  this  way,  the  voltage 
across  c  is  Q/c  and  the  voltage  across 
C  is  QIC,  or,  in  other  words,  the 
voltages  across  the  respective  con- 
densers are  inversely  as  their  capac- 
ities. Any  layer  of  insulation  together 

with  the  adjacent  sheets  of  tin-foil  in  Fig.  21  constitutes  a 
condenser,  and  the  condensers  formed  by  all  the  layers  of  insula- 
tion and  sheets  of  tin-foil  are  in  series.  Therefore  the  voltage 
is  the  same  across  every  layer  if  the  various  capacities  are  equal. 
To  make  the  various  capacities  equal  (with  same  thickness  of 
dielectric  in  each  case)  the  sectional  areas*  of  the  various  layers 
of  dielectric  must  be  the  same,  that  is  to  say,  the  length  parallel 
to  the  rod  of  each  successive  layer  must  be  reduced  in  proportion 
to  the  increasing  circumference  around  the  rod. 


Fg.  22. 


APPENDIX  B.      PROBLEMS. 
CHAPTER  I. 

COSTS. 

1.  Calculate  the  values  of  station  load  factor  corresponding 
to  each  of  the  curves  in  Fig.  5,  to  the  curve  in  Fig.  6,  and  to 
each  of  the  curves  in  Fig.  7. 

2.  From  the  data  given  in  the  table  on  page  12  calculate  each 
item  of  cost  of  operating  the  i5O-kilowatt  plant  at  0.2  load  factor 
and  at  0.8  load  factor. 

3.  From  the  data  given  in  Fig.  8  calculate  the  following  items 
of  cost  of  operating  a  io,ooo-kilowatt  steam  turbine  plant  at 
full  load  and  at  30  per  cent,  load:  (a)  Coal  and  water  [see  page  12 
for  statement  as  to  quality  of  coal  and  cost  of  coal  per  ton]; 
(b)  boiler  room  and  engine  room  labor,  coal  and  ash  handling, 
oil  and  engine  room  supplies ;  and  (c)  fixed  charge. 

4.  A  i5O-kilowatt  lighting  plant  operates  night  and  day  at  0.2 
load  factor  and  the  schedule  of  operation  costs  are  shown  in  the 
table  on  page  12.     It  is  impossible  to  increase  the  lighting  load 
because  the  peak  of  the  load  already  reaches  the  limit  of  overload 
capacity  of  the  plant.     It  is  possible,  however,  to  increase  the 
output  of  the  plant  by  supplying  current  for  motors  off  the  peak 
if  the  motor  rate  is  made  very  low  so  as  to  attract  customers. 
What  would  be  the  cost  to  the  station  per  kilowatt-hour  of  addi- 
tional output  if  the  load  factor  of  the  station  were  raised  to  0.4 
by  supplying  motors  off  the  peak? 

5.  Find  from  the  curve    A    of  Fig.  9  the  probable  peak  load 
of  a  station  supplying  20  residences  in  each  of  which  60  lamps 
are  installed,  50  residences  in  each  of  which  40  lamps  are  installed, 
100  residences  in  each  of  which  20  lamps  are  installed,  and  200 
residences  in  each  of  which  10  lamps  are  installed. 

6.  A  certain  customer  might  be  asked  to  pay  $2.00  per  month 

277 


278  ELECTRIC   LIGHTING. 

"connection"  charge,  his  maximum  demand  is  5  kilowatts  on 
the  peak  for  which  he  might  be  asked  to  pay  at  the  rate  of  $60 
per  kilowatt  per  year,  and  his  yearly  consumption  is  5,000  kilo- 
watt-hours for  which  he  might  be  charged  at  the  rate  of  3  cents 
per  kilowatt-hour.  What  would  be  the  cost  of  electrical  energy 
to  this  customer  per  kilowatt-hour? 

Note. — Compare  table  on  page  19. 

7.  A  small  customer  has  ten  2O-watt  lamps.   Asssuming  10  cents 
per  month  as  a  reasonable  connection  charge  (without  a  meter), 
$60  per  year  per  kilowatt  of  maximum  demand,  and  3  cents  per 
kilowatt-hour  of  consumption  what  would  be  the  equivalent  flat 
rate  for  the  10  lamps,  an  excess  indicator  being  installed  to  limit 
the  maximum  demand  to  160  watts,  the  yearly  consumption  being 
43  kilowatt-hours? 

8.  A  Thomson  watt-hour  meter  without  a   starting  coil   starts  on  a   75-watt 
load.     The  meter  is  adjusted  to  give  a  true  watt-hour  record  when  run  on  a  500- 
watt  load.     What  will  the  instrument  indicate  after  running  for  4  hours  on  a  con- 
stant load  of  200  watts,  running  friction  being  assumed  to  be  equal  to  half  of  start- 
ing friction.     See  note  to  problem  10.     Ans.  702.8  watt-hours. 

9.  The  watt-hour  meter  specified  in  problem  8  is  provided  with  a  starting  coil 
so  as  to  start,  on  no- volt  mains,  when  the  power  delivered  to  the  receiving  circuit 
is  40  watts.     At  what  load  will  the  meter  start  on  55-volt  mains?     See  note  to 
problem  10.     Ans.  66.25  watts. 

10.  The  watt-hour  meter  of  problem  9  is  adjusted  to  record  a  500- watt  load 
correctly  on  no-volt  mains.     At  what  load  will  it  record  correctly  on  55-volt  main? 
Ans.  5,750  watts. 

Note. — The  driving  torque,  not  counting  that  due  to  the  starting  coil,  is  propor- 
tional to  the  watts  delivered  to  the  receiving  circuit,  and  it  may  be  conveniently 
expressed  in  "watts."  The  driving  torque  due  to  the  starting  coil  (with  given 
voltage  between  the  supply  mains)  may  be  expressed  as  the  difference  between  the 
starting  watts  with  and  without  the  starting  coil.  The  running  friction  (a  torque) 
may  be  expressed  as  one  half  the  starting  load  in  watts  without  the  starting  coil. 
The  speed  of  the  meter  may  be  conveniently  expressed  in  "watt-hours  recorded 
per  hour." 

Subtracting  from  the  total  driving  torque  (including  the  torque  due  to  the  starting 
coil)  the  running  friction,  gives  the  net  torque  used  to  overcome  the  retarding  action 
of  the  damping  magnets,  and  the  speed  of  the  meter  is  proportional  to  this  net  torque. 
The  torque  produced  by  the  starting  coil  is  proportional  to  the  square  of  the  voltage 
between  the  mains. 

11.  The  net  assets  of  the  Wallingford  plant  year  after  year 
are  represented  by  the  differences  between  the  ordinates  of  the 


PROBLEMS.  279 

curves  A  and  B  in  Fig.  13,  and  the  capitalization  at  the  begin- 
ning was  $55,000.  Find  the  rate  at  compound  interest  which  is 
represented  by  the  growth  of  the  net  assets  to  $96,881  on  July  31, 
1910  (lof  years  from  the  beginning).  Ans.  5.53  per  cent. 

Note. — This  rate  of  interest  does  not  represent  the  real  profits  of  the  plant; 
to  find  the  real  profits  one  must  take  into  consideration  the  annual  payment  of 
bond  interest  as  explained  in  problem  12.  If  the  Wallingford  plant  continues  in  the 
future  to  make  the  same  profits  it  has  made  in  the  past  then  in  1920  the  net  assets 
will  be  $161,700  and  there  will  remain  $106,700  of  net  assets  after  the  bonds  are 
paid.  Furthermore,  the  accumulated  depreciation  charge  will  in  1920  probably 
amount  to  more  than  the  actual  depreciation  so  that  the  $106,700  will  be  real 
tangible  assets. 

12.  The  Wallingford  plant  has  been  paying  $1,925  annually  as 
interest  on  its  bonds,  beginning  on  August  I,  1900,  so  that  on 
August  i,  1910,  eleven  payments  had  been  made.  Find  the 
accumulated  cash  value  on  August  I,  1910,  of  all  these  payments 
(the  accumulation  being  reckoned  at  3^  per  cent,  compound 
interest),  add  this  to  the  net  assets  on  August  I,  1910,  and  find 
the  rate  at  compound  interest  which  is  represented  by  the  growth 
from  $55,000  in  io|  years.  Ans.  7.9  per  cent. 


CHAPTER   II. 

ELECTRIC   DISTRIBUTION  AND  WIRING. 

13.  A  span,  150  feet  long,  of  hard-drawn  copper  wire,  No.  8  Brown  and  Sharpe 
gauge,  is  to  be  strung  at  a  temperature  of  75°  F.  at  a  place  where  the  winter  tem- 
perature sinks  to  — 20°  F.     The  maximum  tension  of  the  wire  is  to  be  164  pounds. 
Find:  (a)  The  sag  at  —20°  F.;  (6)  the  sag  at  75°  F.,  and  (c)  the  tension  at  75°  F. 
Ans.  (a)  0.86  foot;  (b)  2.86  feet;  (c)  49  pounds. 

14.  Five  hundred  glow  lamps  each  taking  one-half  an  ampere 
at  1 10  volts  are  supplied  with  current  from  a  1 15.5-volt  generator 
at  a  distance  of  1,000  feet  from  the  lamps.     Find:  (a)  The  size 
of  copper  wire  required,  (b)  the  total  weight  of  the  wire,  and  (c) 
the  total  cost  of  the  wire  at   16  cents  per  pound.     Ans.   (a) 
982,000  circular  mils;  (b)  5,950  pounds;  (c)  953  dollars. 

15.  Five  hundred  glow  lamps  each  taking  one-half  an  ampere 
at  no  volts  are  supplied  with  current  from  a  231 -volt  generator 


280  ELECTRIC   LIGHTING. 

at  a  distance  of  1,000  feet  from  the  lamps.  The  Edison  three- 
wire  system  is  used  and  the  system  is  balanced.  Find:  (a)  The 
size  of  copper  wire  required  for  the  outside  mains;  (b)  the  total 
weight  of  all  three  mains,  the  middle  main  having  one-half  the 
sectional  area  of  either  outside  main;  and  (c)  the  total  cost  of 
the  three  mains  at  16  cents  per  pound.  Ans.  (a)  245,500  circular 
mils;  (b)  1,860  pounds;  (c)  298  dollars. 

16.  The  three-wire  system  of  problem  15  supplies  300  lamps 
(150  amperes)  on  one  side  and  200  lamps  (100  amperes)  on  the 
other  side,  all  at  a  distance  of  1,000  feet  from  a  231 -volt  gen- 
erator.    A  balancer  is  used  in  the  station  to  take  care  of  the 
current  in  the  middle  main  and  to  keep  the  voltage  between  the 
middle  main  and  each  outside  main  equal  to  115.5  volts.     Find: 
(a)  The  voltage  across  the  set  of  300  lamps;  and  (b)  the  voltage 
across  the  set  of  200  lamps.     Ans.  (a)  104.5  volts;  (b)  1 15.5  volts. 

Note. — If  the  lamps  above  specified  are  all  exactly  alike  it  is  evident  that  the 
current  in  each  lamp  of  the  300  set  cannot  be  the  same  as  the  current  in  each  lamp 
of  the  200  set.  It  is  usual,  however,  in  wiring  calculations  to  consider  that  lamps 
of  a  given  size  and  type  take  a  definite  amount  of  current  irrespective  of  the  slight 
variations  of  voltage. 

17.  The  three-wire  system  of  problem  15  supplies  300  lamps 
(150  amperes)  on  one  side  and  100  lamps  (50  amperes)  on  the 
other  side,  and  the  total  voltage  of  231  volts  at  the  generator  is 
equally  divided  by  the  balancer  as  explained  in  problem   16. 
Find:  (a)  The  voltage  across  the  set  of  300  lamps;  and  (b)  the 
voltage  across  the  set  of  loo  lamps.     Ans.  (a)  100.1  volts;  (b) 
122. 1  volts. 

18.  A  group  of  ten  lamps,  each  taking  one-half  an  ampere,  is 
ten  feet  distant  from  ii5-volt  mains,     (a)  Find  the  size  of  wire 
required  in  order  to  give  a  drop  of  5  volts,     (b)  What  size  of 
wire  (rubber  insulation)  would  be  required  according  to  the  table 
of  safe  carrying  capacity  given  on  page  55?     Ans.  (a)  14.7  mils 
diameter;  (b)  No.  16  Brown  and  Sharpe  gauge  (51  mils  diameter). 

Note. — It  is  evident  that  a  wire  14.7  mils  in  diameter  would  be  excessively  heated 
by  a  current  of  5  amperes.  Usually  the  size  of  wire  for  supplying  lamps  near  to  the 
generator  or  center  of  distribution  is  determined  by  the  table  of  safe  carrying  ca- 
pacity. 


PROBLEMS.  28l 

The  insurance  rules  forbid  the  use  of  wire  smaller  than  No.  14  Brown  and  Sharpe 
gauge  for  house  wiring. 

19.  A  pair  of  street  mains  leading  out  from  a  central  station 
delivers  50  amperes  of  current  to  a  consumer  at  a  distance  of  200 
feet  from  the  station,  75  amperes  to  a  second  consumer  at  a 
distance  of  350  feet  from  the  station,  and  40  amperes  to  a  third 
consumer  at  a  distance  of  600  feet  from  the  station.     The  station 
voltage  is  115  volts  and  the  voltage  at  the  distant  end  of  mains 
is  no  volts.     Find:  (a)  The  size,  weight,  and  cost  of  mains  of 
uniform  size;  and  (b)  the  size  of  each  section  of  the  mains,  and 
their  total  weight  and  cost,  when  the  size  is  reduced  in  steps  so 
as  to  give  the  specified  voltage-drop  with  a  minimum  amount  of 
copper.     The  cost  of  copper  is  to  be  taken  at  16  cents  per  pound. 
Ans.  (a)  260,300  circular  mils,  946.5  pounds,  151.2  dollars,  (b) 
first  section  319,700  circular  mils,  second  section  267,000  circular 
mils,  third  section  157,400  circular  mils,  868  pounds,  139  dollars. 

Note. — In  estimating  the  distance,  L,  of  the  "center  of  gravity"  of  the  con- 
sumers in  the  above  problem,  one  may  use  one  ampere  as  the  unit  instead  of  one 
lamp. 

20.  An  electric  railway  33,300  feet  in  length  is  divided  into 
three  sections  of  which  the  lengths,  9,000  feet,  10,800  feet  and 
13,500  feet,  are  proportional  to  the  schedule  speeds  of  cars  on 
the  respective  sections  so  that  a  car  running  from  end  to  end  of 
the  line  traverses  each  section  in  10  minutes.     Four  cars  are 
always  on  the  first  section  five  minutes  apart  going  each  way,  two 
cars  are  always  on  the  second  section  ten  minutes  apart  going 
each  way,  and  a  single  car  is  always  on  the  third  section  making 
the  round  trip  in  20  minutes.     Owing  to  frequent  stops  on  the 
first  section  the  cars  taken  an  average  current  of  125  amperes  each, 
on  the  second  section  the  stops  are  less  frequent  and  each  car 
takes  an  average  of  105  amperes,  and  on  the  third  section  the 
stops  are  least  frequent  and  the  car  that  is  always  on  this  section 
takes  an  average  of  95  amperes. 

The  "center  of  gravity"  of  the  four  cars  that  are  always  on 
the  first  section  is  at  the  middle  of  the  section,  the  "center  of 


282  ELECTRIC    LIGHTING. 

gravity"  of  the  two  cars  that  are  always  on  the  second  section  is 
at  the  middle  of  that  section,  and  the  most  unfavorable  position 
of  the  single  car  that  is  always  on  the  third  section  is  when  it  is 
at  the  extreme  end  of  the  line.  Assume,  therefore,  that  500 
amperes  are  delivered  continuously  at  the  middle  of  the  first 
section  (4,500  feet  from  the  city  end),  that  210  amperes  are  de- 
livered continuously  at  the  middle  of  the  second  section  (14,400 
feet  from  the  city  end),  and  that  95  amperes  are  delivered  con- 
tinuously at  the  extreme  end  of  the  line.  If  the  power  house  is 
located  at  the  city  end  of  the  line,  find:  (a)  The  size  of  each 
section  of  the  feeder  to  give  a  total  drop  of  75  volts  at  the  ex- 
treme end  of  the  line  with  a  minimum  amount  of  copper;  and 
(b)  the  total  cost  of  feeder  copper  at  16  cents  per  pound.  Ans. 
(a)  First  4,500  feet  of  feeder  1,980,000  circular  mils,  next 
9,900  feet  of  feeder  1,219,000  circular  mils,  and  remaining  18,900 
feet  of  feeder  680,000  circular  mils;  (b)  16,400  dollars. 

Note. — The  resistance  of  the  bonded  track,  which  is  used  as  a  return  feeder,  is 
very  uncertain  and  it  is  here  to  be  assumed  equal  to  zero  for  the  sake  of  simplicity. 

21.  (a)  Find  the  position  in  which  the  power  house  should  be 
placed  on  the  railway  specified  in  problem  20  in  order  that  the 
feeder  copper  may  be  reduced  to  a  minimum ;  (b)  find  the  size  of 
each  section  of  the  feeder  on  the  assumption  that  the  two  cars  on 
the  middle  section  are  in  the  most  unfavorable  positions,  namely, 
at  the  two  ends  of  the  section,  and  on  the  assumption  that  the  car 
on  the  third  section  is  at  the  extreme  end  of  the  section ;  and  (c) 
find  the  total  cost  of  the  feeder  copper  at  16  cents  per  pound. 
Total  drop  to  each  end  of  the  line  to  be  75  volts.  Ans.  (a) 
10,480  feet  from  the  city  end  of  the  railway;  (b)  first  section 
441,000  circular  mils,  city  end  of  second  section  (1,480  feet) 
485,200  circular  mils,  suburban  end  of  second  section  (9,320 
feet)  536,700  circular  mils,  and  third  section  369,900  circular 
mils;  (c)  7,119  dollars. 

Note. — The  power  house  should  be  placed  at  the  center  of  "gravity  "of  a  system 
in  the  sense  in  which  this  term  is  defined  on  page  62  in  order  that  the  amount  of 
feeder  copper  may  be  a  minimum.  Similarly,  a  center  of  distribution,  from  which 


PROBLEMS.  283 

electric  lamps  are  to  be  supplied  by  street  mains,  should  be  located  at  the  "center 
of  gravity"  of  the  consumers,  each  consumer  being  "weighted"  in  proportion  to  the 
current  delivered  to  him. 

The  feeder  on  city  section  of  9,000  feet  is  assumed  to  be  of  uniform  section  of 
441,000  circular  mils  throughout,  but  it  would  be  advisable  in  fact  to  make  the 
extreme  city  end  of  this  section  of  the  feeder  much  smaller  than  441,000  circular  mils. 

22.  A  nearly  reentrant  row  of   100  lamps,  each  taking  one- 
half  an  ampere,  is  to  be  wired  in  accordance  with  the  return  loop 
scheme,  using  wire  of  uniform  size.     The  row  is  200  feet  long, 
one  end  of  the  row  is  50  feet  from  the  service  point,  and  the 
other  end  of  the  row  is  60  feet  from  the  service  point.     The  vol- 
tage at  the  service  point  is  115  volts.     Find  the  size  of  wire  to 
give   105  volts  at  the  middle  lamp  of  the  row.     Ans.   14,040 
circular  mils  sectional  area. 

Note. — Such  problems  as  this  and  problem  23  are  most  easily  solved  on  the 
assumption  that  the  given  group  of  lamps  is  equivalent  to  a  so-ampere  load  dis- 
tributed with  ideal  uniformity  over  the  whole  length  of  200  feet. 

23.  Find  the  voltage  at  each  end  lamp  in  the  row  specified  in 
problem  22.     Ans.  106.93  volts. 

Note. — The  drop  all  the  way  along  ab   (or  cd)  of  Fig.  35  is  equal  to 

ol    (&=x 

P—    \         (X  -  x)dx 

X  Jx=o 

(as  may  be  understood  from  the  discussion  on  page  65)  and  this  is  equal  to  %pXI. 
The  voltage  across  lamp  at  either  end  of  row  is  the  service  voltage  minus  %pXI, 
minus  the  drop  in  efa,  and  minus  the  drop  in  ge. 

24.  All  the  lamps  except  the  middle  lamp  in  the  row  speci- 
fied in  problem  22  are  turned  off.     Find  the  rise  of  voltage  at 
the  middle  lamp.     Ans.  From  105  volts  to  114.88  volts. 

25.  Find  the  size  of  wire  required  to  supply  the  row  of  100 
lamps  specified  in  problem  22  by  the  simple  parallel  scheme, 
both  service  wires  being  led  from  the  service  point  to  the  nearer 
end  of  the  row:  (a)  when  the  drop  between  the  service  point 
and  the  most  remote  .lamp  is  10  volts;  (b)  when  the  drop  to  the 
most  remote  lamp  exceeds  the  drop  to  the  nearest  lamp  by  the 
amount  (106.93  ~~  IO5)  volts;  and  (c)  when  the  drop  to  the  most 
remote  lamp  is  5  volts.     Ans.  (a)  16,200  circular  mils  sectional 
area;  (b)  56,000  circular  mils;  (c)  32,400  circular  mils. 


284  ELECTRIC   LIGHTING. 

Note. — In  case  (a)  we  have  the  same  total  drop  as  in  problem  22,  but  the  voltage 
at  the  lamps  ranges  from  105  volts  at  the  remote  end  to  111.67  volts  at  the  near 
end  of  the  row,  that  is,  a  range  of  6.67  volts;  whereas  with  the  return  loop  scheme  as 
specified  in  problem  22  the  voltage  at  the  lamps  ranges  from  105  at  the  middle  lamp 
to  a  maximum  of  106.93  volts,  that  is,  a  range  of  only  1.93  volts,  and  the  wire 
in  the  return  loop  scheme  is  the  smaller. 

In  case  (b)  the  voltage  at  the  lamps  has  the  same  range  as  in  problem  22  and  the 
lamps  therefore  would  operate  equally  well  as  in  the  return  loop  scheme  as  specified 
in  problem  22,  provided  the  lamps  are  all  in  use  or  all  out  of  use,  but  the  wire  in 
case  (6)  is  nearly  four  times  as  heavy  as  in  problem  22.  This  shows  in  a  striking  way 
the  saving  of  copper  by  the  return  loop  scheme,  for  the  same  range  of  voltage  among 
the  lamps,  when  the  group  of  lamps  forms  a  nearly  reentrant  row  and  when  the 
lamps  are  always  either  all  on  or  all  off. 

On  the  other  hand,  the  result  of  problem  24  shows  that  the  return  loop  as  speci- 
fied in  problem  22  is  not  at  all  suited  to  the  case  in  which  part  of  the  lamps  in  the 
group  are  turned  off,  the  effect  being  to  cause  a  very  considerable  rise  of  voltage  at 
the  remaining  lamp  (or  lamps). 

26.  A  group  of  50  lamps  each  taking  i.o  ampere  is  to  be 
installed  at  a  distance  of  one  mile  from  a  lighting  station.  It  is 
understood  that  whenever  any  of  the  lamps  are  in  use  all  are 
in  use,  so  that  the  drop  in  the  feeders  which  supply  the  lamps 
may  have  any  value  that  economy  demands.  The  lamps  are 
to  be  operated  for  300  hours  each  year.*  The  cost  of  power 
at  the  station  is  3.5  cents  per  kilowatt-hour,  the  cost  of  copper 
is  1 6  per  cents  per  pound,  the  annual  charge  on  the  cost  of  the 
wire  is  10  per  cent,  (interest  6  per  cent.,  depreciation  3  per  cent., 
and  taxes  I  per  cent.),  and  the  station  voltage  is  125  volts. 
Find:  (a)  The  size  of  the  feeders  to  give  a  balance  between  loss 
of  power  and  cost  of  copper,  and  (b)  the  voltage  at  the  lamps. 
Ans.  (a)  76,370  circular  mils;  (b)  50.45  volts. 

Note  i. — The  only  objection  to  the  application  of  the  economic  principle  of  the 
balance  between  loss  of  power  and  cost  of  copper  to  a  case  like  the  one  here  con- 
sidered is  that  the  voltage  at  the  lamps  may  be  very  different  from  the  voltage  which 
prevails  in  the  other  parts  of  the  lighting  system,  so  that  the  station  management 
would  have  to  be  careful  to  supply  special  lamps  suited  to  the  special  voltage.  It  is 
evident  that  it  is  expensive  at  best  to  supply  the  fifty  lamps  at  a  distance  of  a  mile, 
for,  under  the  conditions  of  problem  26,  it  requires  $391.40  worth  of  copper  with  a 
loss  of  $39.14  worth  of  power  each  year,  and  to  transmit  the  required  power  (2.522 
kilowatts,  or  22.93  amperes  with  no  volts  at  the  lamps)  with  15  volts  drop  would 
take  $892  worth  of  copper  with  a  loss  of  $3.61  worth  of  power  each  year. 

Note  2. — It  is  instructive  to  solve  problem  26  graphically  as  follows:  Assume, 


PROBLEMS.  285 

say,  50,000,  60,000,  70,000,  80,000,  90,000,  and  100,000  circular  mils.  Use  these 
sectional  areas  as  abscissas  of  two  curves,  A  and  B;  the  ordinates  of  curve  A 
representing  the  values  in  dollars  of  the  power  lost  each  year,  and  the  ordinates 
of  curve  B,  representing  the  annual  charge  in  dollars  on  the  total  cost  of  the  copper. 
Then  plot  a  third  curve,  C,  of  which  each  ordinate  is  the  sum  of  the  corresponding 
ordinates  of  curves  A  and  B,  and  the  abscissa  corresponding  to  the  minimum  ordi- 
nate of  this  curve,  C,  is  the  required  sectional  area. 

27.  The  customer  mentioned  in  problem  26  is  to  pay  at  the 
rate  of  n  cents  per  kilowatt-hour  for  all  energy  delivered  to 
his  special  line  in  excess  of  the  usual  5  per  cent,  line  loss.     At 
what  rate  per  kilowatt-hour  must  this  customer  pay  on  the  basis 
of  his  watt-hour  meter? 

28.  A  consumer  pays  10  cents  per  kilowatt-hour  not  only  for 
the  energy  he  uses  in  his  lamps  but  also  for  the  energy  that  is 
lost  in  the  wires  that  lead  from  the  watt-hour  meter  to  his  lamps. 

If  the  customer  uses  his  lamps  2  hours  per  day  the  year  round, 
find  the  size  of  wires  he  should  use  in  his  house,  in  circular  mils 
per  ampere,  for  greatest  economy,  the  cost  of  copper  being  16 
cents  per  pound,  and  the  interest  and  depreciation  being  8  per 
cent.  Ans.  4,507  circular  mils  per  ampere. 

29.  The  cost  of  power  at  the  switch-board  in  an  arc-lighting 
station  is  2  cents  per  kilowatt-hour.     The  plant  supplies  a  current 
of  6.6  amperes  to  a  circuit  of  50  arc  lamps  which  are  operated 
on  a  moonlight  schedule  for  2,160  hours  each  year.     The  cost 
of  copper  is  21  cents  per  pound,  and  the  annual  charge  on  the 
cost  of  the  wire  is  n  per  cent,  (interest  6  per  cent.,  depreciation 
3.5  per  cent.,  and  taxes  1.5  per  cent.).     The  cost  of  the  wire  is 
high  and  its  depreciation  is  large  because  the  wire  is  insulated. 
The  price  of  2L  cents  per  pound  is  on  the  net  weight  of  copper 
in  the  wire  and  this  price  is  intended  to  cover  the  cost  of  the 
insulation.     Find  the  size  of  wire  to  give  a  balance  between  loss 
of  power  and  cost  of  copper.     Ans.  17,040  circular  mils. 

Note. — The  falling  of  an  arc  light  wire  into  the  street  would  be  very  dangerous  on 
account  of  the  high  voltage.  Therefore,  it  is  important  that  an  arc-lamp  circuit  be 
very  substantial.  It  is  usually  not  considered  allowable  for  this  reason,  to  use 
wire  smaller  than  No.  6  Brown  and  Sharpe  gauge  (26,000  circular  mils)  for  an  arc- 
lamp  circuit. 


286  ELECTRIC   LIGHTING. 

30.  Find  the  cost  to  the  station  owners  of  16.5  kilowatts  of 
power  delivered  for  1,200  hours  each  year  at  220  volts  over  a 
special  line  to  a  single  customer  at  a  distance  of  one  mile  from  the 
station,  the  wire  being  of  such  size  as  to  give  a  balance  between 
loss  of  power  and  cost  of  copper.     Determine  the  size  of  wire  on 
the  basis  of  a  6  per  cent,  annual  charge  on  the  cost  of  the  copper  at 
1 6  cents  per  pound,  the  cost  of  power  at  the  switch-board  being 
2.5  cents  per  kilowatt-hour.     Reckon  the  total  cost  of  the  line 
at  2.25  times  the  cost  of  the  copper,  and  reckon  the  total  annual 
cost  of  interest,  depreciation,  taxes,  and  maintenance  of  line  at 
15  per  cent,  of  the  total  cost  of  the  line.     Ans.  $1,176.80  per 
year,  or  about  6  cents  per  kilowatt-hour  delivered. 

31.  Given  ten  groups  of  lamps,  each  group  taking  10  amperes, 
the  groups  being  10  feet  apart.     The  lamps  are  supplied  with 
current  from   U5-volt  mains  according  to  the  wiring  scheme 
shown  in  Fig.  37.     The  end  group,    bb    (see  figure),  is  10  feet 
from  the  mains,  the  point,    pp,    is  70  feet  from  the  mains,  and 
No.  2  Brown  and  Sharpe  gauge  copper  wire  is  used  throughout. 
Make  a  drawing  like  Fig.  22&,  showing  vthe  voltage  at  every 
group  of  lamps.     Sample  answer:  1.964  volts  drop  to  the  group 
of  lamps  which  is  50  feet  from  the  service  point. 

Note. — It  would  be  permissible  for  practical  purposes  to  calculate  drops  to  the 
various  lamps  in  this  problem  on  the  assumption  that  the  lamps  constitute  a  load 
which  is  distributed  with  ideal  uniformity.  It  is  here  intended,  however,  that  the 
drops  be  calculated  as  they  actually  are  and  so  represented  in  the  drawing. 

32.  The  accompanying  figure,  Fig.  $2p,  shows  two  motors, 
M  and  Mr,  two  groups  of  glow  lamps,   L  and   Lf,  and  a  group 
of  arc  lamps,  A,  all  supplied  from  the  H5-volt  service  point,   P. 
The  distances  are  all  so  small  that  the  sizes  of  all  wires  are  to  be 
determined   from   the   table   of  safe  carrying  capacities.     The 
motor,  M,  takes  35  amperes,  the  motor,   Mr ,  takes  18  amperes, 
the  group,     L,    contains  7  half-ampere  lamps,  the  group,     Lr, 
contains  3  half-ampere  lamps,  and  each  arc  lamp  takes  5  amperes. 

(a)  Make  a  sketch  of  Fig.  $2p  and  indicate  the  values  of  the 
current  at  the  points  a,  b,  c,  d,  e  and  /;  (b)  indicate  the  size  of 


PROBLEMS. 


287 


WW 


r 


Fig.  32£. 

each  wire  assuming  rubber  insulated  wire  to  be  used;  (c)  show 
the  location  and  mark  the  current  rating  of  every  fusible  cut-out 
and  branch  block  required  by  the  National  Electrical  Code. 


CHAPTER   IV. 

PHOTOMETRY  AND    ILLUMINATION. 

33.  The  conical  intensity  of  a  beam  of  light  from  a  lamp  is  50 
candle-power.     The  lamp  is  5  feet  from  the  center  of  a  hole  in  a 
wall,  and  the  diameter  of  the  hole  is  3  feet.     Find  the  amount  of 
light  passing  through  the  hole  in  lumens. 

Note. — The  area  of  a  spherical  zone  is  equal  to  the  area  of  the  sphere  multiplied 
by  the  altitude  of  the  zone  and  divided  by  the  diameter  of  the  sphere. 

34.  A  5o-candle-power  lamp  is  at  the  center  of  a  circular  band 
which  is  6  feet  in  diameter  and  one  foot  wide.     Find  the  amount 
of  light  which  falls  on  the  band  in  lumens. 

35.  As  seen  from  a  given  direction,  the  luminous  area  of  a  lamp 
(projected  on  a  plane  at  right  angles  to  the  line  of  sight)  is  0.75 
square  inch  and  the  conical  intensity  of  the  light  in  the  given 
direction  is  150  candle-power.     What  is  the  intrinsic  brightness 
of  the  lamp? 


288  ELECTRIC   LIGHTING. 

36.  Find  the  sectional  intensity  of  the  light  from  a  5O-candle- 
power  lamp  at  a  distance  of  5  feet  from  the  lamp,  expressing  the 
result  in  lumens  per  square  foot  and  in  spherical-candles  per 
square  foot. 

37.  The  intensity  of  illumination  at  a  distance  of  four  feet 
from  a  i6-candle  lamp  is  sufficient  for  easy  reading  of  ordinary 
book  type,     (a)  Find  the  distance  from  a  2O-candle  lamp  at 
which  the  lamp  gives  the  same  intensity  of  illumination;  (b)  ex- 
press this  intensity  of  illumination  in  spherical-candles  of  light 
per  square  foot  of  illuminated  surface;  and  (c)  express  this  in- 
tensity of  illumination  in  luxes.     Ans.  (a)  4.47  feet;  (b)  0.0796 
spherical-candle  per  square  foot;  (c)  12.21  luxes. 

38.  The  glow  lamp  which  is  used  as  a  standard  in  a  Bunsen 
photometer  has  a  candle-power  of  16.8  candles  in  the  direction 
towards  the  photometer  screen.     Another  lamp     B     is  placed 
at  the  other  end  of  the  photometer  bar  and  when  the  screen  is 
adjusted  to  equality  of  illumination  on  both  sides,  it  is  2.61  meters 
from  the  lamp     B,    and  1.80  meters  from  the  standard  lamp. 
What  is  the  candle-power  of     B    in  the*  direction  towards  the 
screen?     Ans.  35.3  candle-power. 

Note. — This  problem  is  to  be  solved  with  the  help  of  the  law  of  inverse  squares. 
Equality  of  illumination  on  the  two  sides  of  the  screen  means  that  the  beams  from 
the  two  lamps  have  the  same  sectional  intensity  at  the  screen. 

39.  Find  the  intensity  of  illumination  in  foot-candles  at  a  point 
on  a  floor  distant  6  feet  horizontally  from  a  lamp  which  is  8  feet 
above  the  floor,  the  candle-power  of  the  lamp  in  the  direction 
towards  the  specified  spot  being  65. 

40.  Let  the  brightness  of  daylight  with  the  sun  in  the  zenith 
be  taken  as  unity.     What  is  the  brightness  of  daylight  when  the 
altitude  of  the  sun  is  75°,  60°,  45°,  30°  and  15°,  above  the  horizon 
respectively,  ignoring  increase  of  atmospheric  absorption  with 
increase  of  zenith  distance  of  the  sun? 

Note. — The  relative  brightness  of  daylight  is  inversely  proportional  to  the  area 
of  country  covered  by  a  beam  of  sunlight  of,  say,  one  square  mile  in  sectional  area, 
and  this  is  inversely  proportional  to  the  sine  of  the  sun's  altitude  above  the  horizon. 

41.  A  certain  photographic  lens  gives  a  good  photograph  with 


PROBLEMS.  289 

an  exposure  of  1/50  second  when  the  sun  is  75°  above  the  horizon. 
What  exposure  would  be  required  with  the  same  lens  when  the 
sun  is  5°  above  the  hprizon,  ignoring  increase  of  atmospheric 
absorption  with  increase  of  zenith  distance  of  sun? 

42.  A  direct-current  arc  lamp  gives  the  following  distribution 
of  candle-power: 


Angle  from  vertical. 

10° 

20° 

30° 

40° 

SQ° 

60° 

TOO 

80° 

Candle-power  

290 

440 

670 

i,  080 

1,220 

i,  080 

795 

580 

Calculate  the  intensities  of  illumination  at  points  along  a  level 
open  street  distant  h  tan  10°,  h  tan  20°,  h  tan  30°,  etc.,  hori- 
zontally from  the  lamp:  (a)  When  the  height  h  of  the  lamp 
above  the  street  is  15  feet,  and  (b)  when  the  height  h  of  the 
lamp  above  the  street  is  50  feet.  Express  the  intensities  of 
illumination  in  foot-candles. 

Plot  two  curves  showing  horizontal  distances  from  the  lamp 
as  abscissas  and  intensities  of  illumination  as  ordinates. 

43.  A  beam  of  light  consisting  of  parallel  rays  has  a  sectional 
intensity  of  100  foot-candles.     Find  the  conical  intensity  of  the 
beam  after  it  passes  through  a  lens  of  which  the  focal  length  is 
1 8  inches. 

44.  An  open-arc  lamp  is  placed  at  a  distance  of  five  feet  from  a 
converging  lens,  and  an  image  of  the  arc  is  formed  at  a  distance 
of  one  foot  beyond  the  lens.     The  light  from  the  lamp  has  a 
conical  intensity  of  2,500  candles.     Assuming  that  the  luminous 
surface  of  the  lamp  is  negligibly  small,  and  ignoring  loss  of  light 
at  the  lens  by  reflection  and  absorption,  find  the  conical  intensity 
of  the  beam  beyond  the  image.     Ans.  100  candles. 

45.  Two  lamps  A   and   B  are  placed  at  the  ends  of  a  Bunsen 
photometer  bar,  and  the  photometer  screen  is  adjusted  to  give 
equality  of  illumination  on  its  two  sides.     The  screen  is  then 
one  meter  from  lamp   A   and  3  meters  from  lamp   B.     A  lens  of 
which  the  focal  length  is  25  centimeters  is  placed  50  centimeters 
Jrom  lamp  B,  and  the  screen  is  left  in  its  original  position.     Find 


290  ELECTRIC   LIGHTING. 

how  far  lamp  A  must  be  placed  from  the  screen  to  give  equal 
illumination  on  the  two  sides  of  the  screen,  neglecting  losses  of 
light  in  the  lens.  Ans.  0.67  meter. 

46.  An  acetylene  flame  is  placed  at  the  focal  point  of  a  lens 
which  is  8  inches  in  diameter  and  the  focal  length  of  the  lens  is 
25  inches.     The  luminous  area  of  the  flame  is  0.7  square  inch. 
Find  the  approximate  candle-power  of  the  light  beyond  the  lens. 

47.  The  powerful  arc  lamp  of  a  searchlight  emits  a  beam  of 
which  the  conical  intensity  is  10,000  candle-power.     The  lumi- 
nous area  of  the  arc  is  o.i  square  inch,  the  diameter  of  the  search- 
light lens  is  12  inches  and  the  focal  length  of  the  searchlight  lens 
is  25  inches.     What  is  the  approximate  conical  intensity  of  the 
searchlight  beam? 

48.  A  35.3-candle-power  lamp  is  placed  at  a  distance  of  35  inches 
from  the  center  of  a  large  mirror  which  reflects  the  light  from  the 
lamp  along  a  photometer  bar  towards  the  photometer  screen, 
and  when  the  screen  is  adjusted  to  give  equal  illumination  on  its 
two  sides  it  is  92.5  inches  from  the  standard  lamp  and  91  inches 
from  the  center  of  the  mirror.     The  candle-power  of  the  standard 
lamp  is  1 6. 8  in  the  direction  towards  the  photometer  screen. 
Find  the  factor  by  which  the  apparent  candle-power  of  any  lamp, 
when  measured  by  the  light  reflected  from  the  above  mirror  must 
be  multiplied  in  order  to  correct  for  the  loss  of  light  at  the  mirror. 
Ans.  1.13. 

49.  Calculate  the  mean  spherical  candle-power  of  the  bare 
glow-lamp  from  data  given  in  Fig.  65.     Ans.  13.33  candle-power. 

Note. — Solve  this  problem  by  the  method  explained  at  the  top  of  page  114. 

50.  Construct  a  Rousseau  diagram  for  the  candle-power  curve 
shown  in  Fig.  65,  and,  if  a  planimeter  is  available,  measure  the 
area  of  curve  c'c'c'  (see  Fig.  72)  and  calculate  the  mean  spherical 
candle-power  of  the  lamp. 


PROBLEMS.  291 

CHAPTER  V. 

ELECTRIC  LAMPS.  LAMP  SHADES  AND  REFLECTORS. 

51.  A  closet  or  cellar  lamp  is  used  on  the  average  one  minute 
per  day  and  energy  costs  10  cents  per  kilowatt-hour.     Compare 
the  yearly  cost  (including  interest  on  cost  of  lamp)  of  using  a 
2O-candle-power  (5O-watt)  carbon-filament  lamp  and  a  6o-watt 
tungsten-filament   lamp.     Assume   that   the   tungsten  lamp   is 
broken  once  every  two  years  by  rough  handling. 

Note. — The  table  on  page  135  gives  all  the  data  required  for  the  solution  of  this 
problem. 

52.  From  the  tables  on  pages  135  and  167  find  the  annual 
cost  of  producing  13,333  lumens  6  hours  per  day  for  300  days 
per  year  (see  example  on  page  166)  by  6o-watt  tungsten  lamps 
and  by  5O-watt  metalized  carbon  lamps,  the  cost  of  energy  being 
8  cents  per  kilowatt-hour.     Include  interest  at  6  per  cent,  per 
year  on  cost  of  lamps  and  assume  no  breakage  due  to  rough 
handling. 

53.  Find  the  annual  cost  13,333  lumens  produced  by  6o-watt 
tungsten  lamps  for  1,800  hours  per  year  when  energy  costs  2 
cents  per  kilowatt-hour  and  when  8  Cents  per  kilowatt-hour — 
lamps  to  be  burned  at  top-efficiency  and  at  bottom-efficiency  in 
each  case.     Include  interest  on  first  cost  of  lamps  at  6  per  cent, 
and  neglect  breakage. 

Note. — See  tables  on  pages  167,  139  and  135. 

CHAPTER  VI. 

INTERIOR   ILLUMINATION. 

54.  Half  the  light  from  a  lamp  is  reflected  from  the  walls  of  a 
room.     When  this  reflected  light  again  strikes  the  walls  half  of  it 
is  reflected  and  so  on.     How  much  light  is  there  crossing  and 
re-crossing  the  room  expressed  in  terms  of  the  amount  of  light 
coming  directly  from  the  lamp? 

55.  The  mean  distance  across  the  room  in  problem  54  is  20  feet.     What  fraction 
of  a  second  elapses  after  turning  on  the  lamps  until  the  light  in  the  room  has 
cached  1023/1024  of  its  final  steady  value? 


ELECTRIC    LIGHTING. 


CHAPTER  VII. 

STREET   ILLUMINATION. 

55.  Using  the  table  on  page  175  find  the  distance  apart  of 
lamps  No.  3,  No.  4  and  No.  7  to  give  0.05  foot-candle  normal  to 
beam  (due  to  each  lamp)  at  a  point  midway  between  the  lamps 
when  the  lamps  are  hung  24  feet  above  the  street. 

56.  Using  the  table  on  page  178  find  distance  apart  of  350- 
candle-power  tungsten  lamps  (equipped  like  Fig.   106)  to  give 
0.05  foot-candle  normal  to  beam  (due  to  each  lamp)  at  a  point 
midway  between  lamps  when  the  lamps  are  hung  24  feet  above 
the  street. 

57.  The  dimensions  of  a  certain  city  block  are  shown  in  Fig. 
Find  the  minimum  mean  value  of  normal  illumination 


1 

L 

X                       OO° 

X 

XT 

he-* 

{ 

a 

1 
1 
| 

J375  feet 

i 

x                   a     o      Q 

X 

jr. 

! 

600  feet 

Fig.  57  p. 

(/„)    and  find  annual  cost  per  mile  of  street  with  4,000  hours  of 
service  per  year  and  energy  at  3  cents  per  kilowatt-hour : 

(a)  With  6.6  magnetite-arc  lamps  at  crosses  and  35o-candle- 
power  tungsten  lamps  at  circles. 

(b)  With  4-ampere  magnetite-arc  lamps  at  crosses  and  200- 
candle-power  tungsten  lamps  at  circles. 

(c)  With  2OO-candle-power  tungsten  lamps  at  crosses  and  50- 
candle-power  tungsten  lamps  at  squares. 

Note. — By  mean  value  of  In  at  a  given  point  on  the  street  it  is  here  intended 
to  refer  to  half  the  sum  //  +  /„",  where  /»'  and  In"  refer  to  the  two  lamps 
between  which  the  given  point  lies. 


PROBLEMS.  293 

Assume  all  lamps  to  be  24  feet  high  and  plot  curve  for  /,/  and  Jn"  with  the 
help  of  the  tables  on  pages  1 75  and  1 78.  Then  plot  the  curve  of  which  the  ordinates 
represent  \(In'  +  In")-  Assume,  in  the  absence  of  more  exact  data,  that  mainte- 
nance, first  cost,  interest  and  depreciation  are  the  same  for  a  zoo-candle-power 
tungsten  lamp  as  for  a  35o-candle-power  lamp. 

In  reckoning  the  cost  per  mile  of  street  note  that  four  crosses  and  four  circles 
(or  four  crosses  and  ten  squares)  represent  3,900  feet  of  street  in  Fig.  STP- 

A  serious  objection  to  the  use  of  many  small  lamps  along  a  street  is  the  cost  of 
the  lamp-supporting  structure.  The  cost  of  this  structure  is  not  to  be  considered 
in  this  problem. 

CHAPTER  VIII. 

ELECTROLYSIS  AND    BATTERIES. 

58.  The  anode  of  an  electrolytic  cell  is  a  copper  rod  I  inch 
in  diameter  and  the  cathode  is  a  hollow  copper  cylinder  6  inches 
inside  diameter;  the  two  electrodes  are  co-axial  and  they  stand 
vertically  in  an  electrolyte  8  inches  deep.     A  current  of  5  amperes 
flows  through  the  cell.     Find  the  current  density  at  the  cathode 
and  the  current  density  at  the  anode. 

59.  Calculate  the  number  of  cubic  centimeters  of  oxygen  and 
the  number  of  cubic  centimeters  of  hydrogen  liberated  in  one 
hour  by  a  current  of  one  ampere;  inert  electrodes  being  used  in 
dilute  sulphuric  acid  or  in  a  solution  of  potassium  or  sodium 
hydrate.     The  gases  being  reckoned  dry  at  o°  C.  and  760  milli- 
meters pressure.     Ans.  209  cubic  centimeters  of  oxygen  and  418 
cubic  centimeters  of  hydrogen. 

Note. — The  density  of  dry  oxygen  at  o°  C.  and  760  millimeters  pressure  is  0.00143 
grams  per  cubic  centimeter  and  the  density  of  dry  hydrogen  at  o°  C.  and  760 
millimeters  prssure  is  0.0000902  grams  per  cubic  centimeter.  The  atomic  weight 
of  silver  is  107.93  and  the  atomic  weight  of  hydrogen  is  i.oi  (o  =  16). 

59.  An  electrolytic  generator*  for  oxygen  and  hydrogen  re- 
quires 3  volts  per  cell.  Find  the  cost  of  one  cubic  foot  of  oxygen 

*  A  good  form  of  electrolytic  generator  for  hydrogen  and  oxygen  is  described  by 
W.  S.  Franklin,  Physical  Review,  Vol.  IV,  pages  61-64,  July,  1896.  A  large  gener- 
ator of  this  type  using  cast  iron  frames  and  sodium  hydrate  solution  has  been  in  use 
for  about  13  years  by  the  Nernst  Lamp  Company;  and  the  depreciation  and  repairs 
have  been  negligibly  small.  The  generator  consists  of  35  cells  in  series  supplied 
with  current  from  no-volt  mains.  See  American  Electrician,  Vol.  XI,  pages  526- 
527,  November,  1899. 


294  ELECTRIC   LIGHTING. 

and  two  cubic  feet  of  hydrogen  when  energy  costs  2  cents  per 
kilowatt-hour  making  no  allowance  for  interest  on  cost  of  gen- 
erators and  no  allowance  for  depreciation  and  repairs  of  generator. 

60.  The  heat  of  combustion  of  one  gram  of  hydrogen  is  34,700 
calories.     What  fraction  of  the  energy  delivered  to  the  generator 
of  problem  59  is  represented  by  or  tied  up  in  the  oxygen  and 
hydrogen  produced?     Ans.  50.7  per  cent. 

61.  The  cost  of  gravity-cell  zinc  is,  say,  6  cents  per  pound,  and 
the  cost  of  copper  sulphate  crystals  (CuSO4  +  5^0)  is,  say, 
6.5  cents  per  pound.     Half  of  the  materials  consumed  in  a  gravity 
cell  is  wasted  by  local  action  and  about  one  third  of  the  zinc  is 
left  as  scrap  and  is  worth  about  2  cents  per  pound.     Furthermore 
the  copper  which  is  deposited  on  the  cathode  is  worth,  as  scrap, 
about  10  cents  per  pound.     The  terminal  electromotive  force  of 
the  cell  while  it  is  delivering  0.16  ampere  is  about  0.72  volt. 
What  is  the  cost  per  kilowatt-hour  of  the  output  of  the  cell  making 
no  allowance  for  cost  of  labor?     Ans.  $1.64. 

62.  The  electromotive  force  of  a  gravity  cell  is  1. 08  volts. 
Find  the  rise  of  temperature  when  10  grams  of  finely  divided  zinc 
are  stirred   into  2,000  cubic  centimeters  (approximately  2,000 
grams)  of  dilute  copper  sulphate  solution. 

Note. — The  specific  heat  of  dilute  copper  sulphate  solution  is  sensibly  the  same 
as  the  specific  heat  of  water.  In  a  Daniell  cell  (gravity  cell)  arranged  to  have  no 
local  action  the  whole  of  the  chemical  energy  is  converted  into  electrical  energy. 

62.  A  lead  storage  cell  delivers  10  amperes  for  8  hours.     Find 
the  increase  of  weight  of  each  electrode.     Ans.  The  positive 
electrode  gains  0.2105  pound  and  the  negative  electrode  gains 
0.3232  pound. 

63.  The  storage  cell  specified  in  problem  62  contains  4,000 
cubic  centimeters  of  dilute  sulphuric  acid  of  which  the  density  at 
1 8°  C.  is  1.700  grams  per  cubic  centimeter  when  the  cell  is  fully 
charged.     Find  the  density  of  the  electrolyte  (at  18°  C.)  after 
the  cell  has  delivered  10  amperes  for  8  hours.     Ans.  1.1286  grams 
per  cubic  centimeter. 

Note. — For  the  solution  of  this  problem  the  following  table  is  needed. 


PROBLEMS.  295 

DENSITY  OF  DILUTE  SULPHURIC  ACID  IN  GRAMS  PER  CUBIC  CENTI- 
METER  AT    1 8°   C. 

Percentage  Strength.  Density. 

o  0.9986 

10  1.0673 

2O  I.I4I4 

30  1. 221 

Percentage  strength  in  this  table  means  the  number  of  grams  of  H2SCU  in  100 
grams  of  the  solution. 

To  solve  the  problem  find  grams  of  H2SO4  and  grams  of  H2O  in  the  solution  at 
the  beginning. 

Then  find  grams  H2SO4  taken  from  the  solution  and  grams  of  I^O  given  to  the 
solution  by  the  discharge. 

Then  find  percentage  strength  of  solution  after  discharge  and  find  density  from 
table. 


INDEX. 


Absorption  coefficient,  definition  of,  162 
coefficients,  table  of,  100 
of  light,  99 
Acuity,  visual,  156 
Alternating  current  lines,  77 
Anion,  definition  of,  185 
Anode,  definition  of,  185 
Arc  lamp,  the,  126 

mechanism,  128 
lamps,  129 

and  glow  lamps  compared,  143 
cost  of  lighting  by,  147 
luminous,  130 
magnetite,  130 
the  flame,  130 
for  street  lighting,  173 
the  electric,  126 
the  luminous,  126 

Balancers  for  three-wire  systems,  42 

Batteries,  184 

Battery,  storage.     See  storage  battery. 

the  primary.     See  voltaic  cell. 
Bichromate  cell,  the,  197 
Block  signalling  for  railways,  252 

vision  and  detail  vision,  171 
Booster,  the,  220 

the  negative,  224 
Boosters,  automatic,  220 
Brilliancy  of  a  lamp,  intrinsic,  90 
Bunsen  photometer,  the,  105 

Cable  insulation,  graded,  263 
Candle  power  curves,  109 

unit,  definition  of,  89 
Carbon  arc  lamp,  intensified,  158 

filament  lamp,  the,  134 
Carcel  lamp,  the,  89 
Carrying  capacity,  safe,  of  wires,  54 
Cathion,  definition  of,  185 
Cathode,  definition  of,  185 
Chemical    calculations    in    electrolysis, 
187 

work  and  heat,  190 
Closed  circuit  cells,  199 
Composite,  the  railway,  245 

2-wire,  the,  248 
Condenser  type  of  insulator,  275 


Conical  intensity,  change  of,  by  lenses, 

99 

of  light  beam,  89 

Connection  cost  of  electric  service,  16 
Constant  current  transformer,  the,  182 
Consumption  cost  of  electrical  service, 

17 

Cooper-Hewitt  lamp,  the,  131 
Copper  oxide  cell,  the,  200 
Corona  formation    as    a    factor    deter- 
mining the  size  of  wires,  70 
Cosine  law,  Lambert's,  97 
Cost,  comparative,  of  electric  lamps,  146 
of  electric  service,  16 
of  electrical  power,  5 
of  power,  influence  of  load  factor 

on,  7 
of  steam  power,  2 

Daniell  cell,  the,  200 
Decomposition  voltage,  190 

voltages,  table  of,  191 
Demand  cost  of  electric  service,  17 
Density  of  current  in  electrolysis,   186 
Deterioration  factors  of  lamps,  149 
Detail  vision  and  block  vision,  171 
Dielectric  stresses,  257 
Diplex  telegraph,  230 
Dissociation  theory  of  electrolysis,  185 
Distribution  of  light  around  a  lamp,  108 

series  and  parallel  systems  of,  36 
Diversity  factor,  the,  14 
Double  current  generator,  the,  42 
Dry  cell,  the,  201 

Duplex  and  quadruplex  on  simplex  and 
composite  circuits,  252 

telegraph,  228 

Edison  Lalande  cell.     See  copper  oxide 

cell, 
storage  cell.     See  storage  cell,  the 

nickel-iron. 

three-wire     generators     and     bal- 
ancers, 42 

3-wire  system,  the,  39 
Electrical  power,  cost  of,  5 
Electric  arc,  the,  126 

code,  the  national,  74 


296 


INDEX. 


297 


Electric  furnace,  255 

plant  of  Wallingford,  Conn.,  27 

railroads,  255 

service,  cost  of,  16 
rates  for,  18 

welding,  255 

Electrochemical    equivalent,    definition 
of,  187 

unit  of  work,  189 
Electrode,  definition  of,  184 

polarization,  192 
Electrolysis,  184 

chemical  calculations  in,  187 

dissociation  theory  of,  185 
Electrolyte,  definition  of,  184 
Electrolytic  cell,  definition  of,  184 
Electromagnetic  ore  concentration,  255 
Extensive  shades,  152 

Faraday,  definition  of  the,  189 

Fechner's  ratio,  107 

Fire  alarm  and  police  telegraph,  255 

Flame  arc  lamps,  130 

Flat  rate  system,  the,  20 

Flicker  photometer,  the,  116 

Floating  battery,  the,  223 

Flux,  of  light,  measurement  of,  112 

Focussing  shades,  152 

Foot-candle,  definition  of,  91 

Fuller  cell,  the,  198 

Furnace,  electric,  255 

Gauss'  theorem,  258 

Glare,  discussion  of,  158 

Globe  photometer,  the,  123 

Globes  and  shades  for  lamps,  151 

Glow  lamp  ratings,  138-143 

the,  133 

lamps  and  arc  lamps  compared,  143 
cost  of  lighting  by,  135 
for  street  lighting,  176 

Graded  cable  insulation,  263 

Gram-val,  definition  of  the,  189 

Gravity  cell,  the,  200 

Grenet  cell,  the,  197 

Heat  and  chemical  work,  190 
Hefner  lamp,  the,  88 

unit,  definition  of,  89 
Holophane  reflector,  the,  154 

Illumination  and  photometry,  86 

calculation  of,  168 

intensities  of,  for  various  kinds  of 
service,  164 

intensity  of,  95 

oblique,  95 

of  a  room,  156 
Illuminometer,  the,  119 


Incandescent  lamp.     See  glow  lamp. 

Indirect  system  of  lighting,  the,  160 

Induction  watt-hour-meter,  the,  23 

Insulation  of  pole  line,  72 

Insulator,  condenser  type,  275 

Intensified  arc  lamp,  158 

Intensities  of  illumination  required  for 

street  lighting,  172 
Intensity  of  illumination,  definition  of, 

95 

Intensive  shades,  152 
Interference  of  lines,  83 
Intrinsic  brilliancy  of  a  lamp,  90 
Ions,  definition  of,  186 

Kelvin's  law,  66-70 

Lambert's  cosine  law,  97 

Lamp  globes,  shades  and  reflectors,  151 

intrinsic  brilliancy  of  a,  90 
Lamps,  choice  of  size  of,  168 

comparative  cost  of  electric,  146 

standard,  88 
Law,  Lambert's  cosine,  97 

of  inverse  squares,  the,  92 
LeClanche  cell,  the,  201 
Lenses,  change  of  conical  intensity  by, 

99 
Light,  absorption  of,  99 

and  radiant  heat,  86 

conical  intensity  of,  89 

distribution  of,  around  a  lamp,  108 

flux,  measurement  of,  112 

luminous  intensity  of,  87 

physical  intensity  of,  86 

sectional  intensity  of,  89 

units,  88,  89 
Lighting  by  the  indirect  system,  160 

cost  of,  by  arc  lamps,  147 

by  glow  lamps,  135 
Lightning  protection,  255 

rods,  255 

Line  interference,  83 
Load     factor,     influence    on    cost    of 

power,  7 
of  customers,  14 
Local  action  and  voltaic  action,  198 

circuit,  the,  226 
Lumen,  definition  of,  90 
Luminous  arc  lamps,  130 
lamp,  the,  127 

intensity  of  light,  87 
Lux,  definition  of,  91 

Magnetite  arc  lamps,  130 
Manganese  dioxide  cell,  201 
Maximum  demand  meter,  the,  26 
Mercury  vapor  lamp,  131 
rectifier,  the,  181 


298 


INDEX. 


Meter  for  maximum  demand,  26 

the  watt-hour,  21 
Meter-rate  system,  the,  20 
Motor-generator  balancer,  42 

National  electric  code,  the,  74 
Negative  booster,  the,  224 
Nernst  lamp,  the,  134 
.Neutral  relay,  231 

Oblique  illumination,  95 
Open  circuit  cells,  199 
Ore  concentration,  255 
Ozone,  255 

Parallel   and   series   systems   of   distri- 
bution, 36 

Pentane  lamp,  the,  88 
Phantom  circuit,  the,  243 

on  two  2-wire  composites,  248 
Photometer,  the,  87,  105 

the  Bunsen,  105 

the  flicker,  116 

the  globe,  123 

laboratory  type,  117 

portable  type,  119 
Photometry,  and  illumination,  36 
Polarization  of  electrode,  192 

of  voltaic  cell,  196 
Polarized  relay,  the,  231 
Pole  line  insulation,  72 
Power,  cost  of,  2 

cost  of,  influence  of  load  factor  on,  7 
Primary  battery,  the,  194 
Printing  telegraph,  234 
Prismatic  glass  reflector,  the,  154 

Quadruplex  telegraph,  233 

and  duplex  on  simplex  and  com- 
posite circuits,  252 
Quartz  lamp,  mercury  vapor,  133 

Radiant  heat  and  light,  87 
Railroads,  electric,  255 
Railway  block  signalling,  252 

composite,  the,  245 
Rates  for  electric  service,  18 
Rating  tungsten  lamps,  three-efficiency 

scheme  of,  139 

Reactance  drop  and  resistance  drop,  78 
Reactances  of  line,  table  of,  79 
Rectifier,  the  mercury  vapor,  181   • 
Reflection  coefficients,  table  of,  100 
Reflectors  and  shades  for  lamps,  151 
Relay,  neutral,  231 

polarized-,  231 
Relays,  telegraph,  226 
Resistance  drop  and  reactance  drop,  78 
Return  loop  scheme,  64 


Rousseau's  diagram,  114 

Safe  carrying  capacity  of  wires,  54 
Search  light,  the,  102 
Sectional  intensity  of  light  beam,  89 
Series   and   parallel   systems   of   distri- 
bution, 36 

Service,  electric,  rates  for,  18 
Shades  and  reflectors  for  lamps,  151 
Sharp-Millar  photometer,  the,  119 
Simplex  blocks  in  series,  248 
circuit,  the,  246 
on  phantom,  247 
Size  of  lamps,  choice  of,  168 
Solid  angle,  unit  of,  90 
Sounders,  telegraph,  226 
Spectrophotometer,  the,  125 
Spherical  angle,  definition  of,  89 

candle,  unit  of,  90 
Standard  lamps,  88 
Steam  power,  cost  of,  2 
Storage  batteries,  control  of,  217 

use  of,  214 
battery,  202 

the  floating,  223 

the    lead,     management     and 

care  of,  211 
cell,  the,  202 

the  lead,  204 
the  nickel-iron,  205 
cells,  costs  and  weights  of,  208 
Strain  insulator,  the,  73 
Street  lighting,  171 

by  arc  lamps,  173 
by  glow  lamps,  176 
intensities  of  illumination  for, 

172 

systems  of,  179 

Stresses,  mechanical,  in  aerial  wires,  46 
Submarine  telegraph,  235 
Suspension  insulator,  the,  73 
Syphon  recorder,  238 
Systems  of  street  lighting,  179 

Table  of  absorption  coefficients,  100 
of  carrying  capacities  of  wires,  55 
of  coefficients  of  reflection,  100 
of  decomposition  voltages,  191 
of  line  reactances,  79 
resistances  of  wires,  75 

Tantalum  lamp,  the,  134 

Telegraph,  diplex,  230 
duplex,  228 

fire  alarm  and  police,  255 
Morse,  the,  226 
printing,  the,  234 
quadruplex,  233 
recorder,  the  syphon,  238 
relays  and  sounders,  226 


INDEX. 


299 


Telegraph,  submarine,  235 

way  stations,  227 

wireless,  255 
Telephone,  the,  238 

calls,  251 

receiver,  239 

transmitter,  238 

Thomson  watt-hour-meter,  the,  22 
Three-efficiency  scheme  of  rating  tung- 
sten lamps,  139 

Three- wire    generators  and    balancers, 
42 

system,  Edison,  the,  39 
Transformer,  constant  current,  the,  182 
Tungsten  lamp,  the,  134 

lamps,    three-efficiency   scheme   of 

rating,  139 
Twilight  vision,  171 
Two-rate  meter,  the,  26 

Ulbricht's  globe  photometer,  123 

Vernon-Harcourt  lamp,  the,  88 

Visual  acuity,  156 

Voltage  drop  as  a  factor  in  determining 

size  of  wires,  54 
of  decomposition,  190 


Voltaic  action  and  local  action,  198 
cell,  the,  194 

the  bichromate,  197 

the  copper  oxide,  200 

the  dry,  201 

the  Fuller,  198 

the  Grenet,  197 

the  LeClanche,  201 

the  manganese  dioxide,  201 

polarization  of,  196 

regeneration  of,  202 
cells,  open  circuit  and  closed  circuit, 
199 

Wallingford  electric  plant,  the,  27 
Watt-hour-meter,  the,  21 

the  induction,  23 

the  Thomson,  22 

the  two-rate,  26 
Way  stations,  227 

in  general,  250 
Welding,  electric,  255 
Wire  calculations,  58-70 

for  alternating  current,  77-84 
Wireless  telegraph,  255 
Wire  table,  75 

Wires,  aerial,  mechanical  stresses  in,  46 
Working  plane,  definition  of,  165 


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